Analyzing energy-saving options in greenhouse cultivation using a simulation model  Nfrv^  Zwart  Analyzing energy-saving options in greenhouse cultivation using a simulation model  Promotoren:  Dr. Ir. G.P.A. Bot Hoogleraar in de Technische Natuurkunde Dr. Ir. L. Speelman Hooglereaar in de Landbouwmechanisatie en Bedrijfsuitrusting  Analyzing energy-saving options in greenhouse cultivation using a simulation model  H.F. de Zwart  Proefschrift ter verkrijging van de graad van doctor in de landbouw- en milieuwetenschappen, op gezag van de rector magnificus, Dr. CM. Karssen, in het openbaar te verdedigen op vrijdag 19april 1996 des namiddags om half twee in de aula van de Landbouwuniversiteit te Wageningen  CIP-DATA KONINKLIJKE BIBLIOTHEEK, DEN HAAG Zwart, H.F. de Analyzing energy-saving potentials in greenhouse cultivation using a simulation model / H.F. de Zwart. [S.l.rs.n.].111. Thesis Landbouwuniversiteit Wageningen. -WithRef. -With summary inDutch ISBN 90-5485-533-9 NUGI 849 Subject headings: energy saving / greenhouse climate simulation  Cover illustration: C.P. de Bruijne  This thesis is also available as a publication nr. 96-5 of the DLO Institute of Agricultural and Environmental Engineering (IMAG-DLO), P.O. Box 43,NL-6700 AA Wageningen, The Netherlands  Stellingen 1. Bijdeberekeningvandewarmtebehoefte vankassennatoepassingvan kasomhullingsmaterialenmeteenhogeisolatiewaardemoetterdege rekeningwordengehoudenmetdevochthuishouding. ditproefschrift 2. Realisatie vandedoelstellingvoordeenergie-efficientie, zoals geformuleerd indemeerjarenafspraak-energie, zalbij dehuidigetrendvanhet toenemendareaalonderglasenhetstijgend gemiddeld verbruikperm2 ertoe leidendatdeC02-doeIstelIingzoalsgeformuleerd inhetNMP-plus nietwordtgehaald. ditproefschrift 3. Het'multi-node'modelvooreengestratificeerde warmte-opslagtankisniet teparametriserennaarfysischmeetbaregrootheden. ditproefschrift 4. Window-functions zoalsgebruiktvoordebeschrijving vanhetventilatiedebietdoorraam-openingeninkassenmoetenwordenopgevatals complexe overdrachtsfuncties. T. deJong,1990, Naturalventilationoflargemulti-spangreenhouses. ProefschriftLandbouwuniversiteit Wageningen 5. Dehuidigewijze vannormerenvanhetjaarlijks gasverbruikmetbehulp vanhetaantal graaddagen resulteert ineentegrote correctiefactor. N.J.A. vander Veldenet. al, 1996, Energieindeglastuinbouwvan Nederland; ontwikkelingen indesectorenopdebedrijvent/m 1994 6. Heteco-keurmerkisopchemischgebiedzeerstringent maarhanteertop fysisch gebied eenvergaand laissez-faire beleid. J.G.Bokhorst, 1995, BiologischekasgroenteteeltLouisBolklnstituut, Driebergen 7. De'CapsLock'toetsvandePCwordtdoorallegangbareprogrammatuur gei'nterpreteerdals'CaseInverse'enheeft daarmeeeenoverbodige, meestalzelfs lastige functie toegekend gekregen. 8. Inverband metpapierbesparing zoudenkopieermachinesdefault op 'tweezijdigafdrukken' moeten staan  9. Omdathetuitrijden vaneenambulance inderegelvoorbode isvaneen moeilijke periodeinhetlevenvanhetslachtoffer endiensverwanten zou desirenebetergebruik kunnen makenvaneenmineurtoonladderdanvan denutoegepaste majeur toonladder. 10.EenLet-systeem (Local ExchangeandTradingSystem)iseensympathiek besloten zwartgeld circuit. De Volkskrant, 15maart 1996 11. HetnoemenvandegarantiedatdeInterlinernietvoordeaangegeven tijd vertrekt alse'envandeplus-puntenvandezevormvanopenbaar vervoer zegtveeloverdekwaliteitvanander busvervoer. BrochureInterliner, november 1995 Stellingenbehorendebijhetproefschrift 'Analyzingenergy-saving optionsin greenhousecultivation usingasimulation model', H.F.deZwart,Wageningen, 19april 1996  ABSTRACT  Hendrik Feije deZwart, 1996,Analyzing energy-saving potentials in greenhouse cultivation using a simulation model. Ph.D. Dissertation, Landbouwuniversiteit, Wageningen. Alsoavailable asapublication oftheDLO Institute of Agricultural and Environmental Engineering (IMAG-DLO), Wageningen, The Netherlands  GreenhouseHorticulture intheNetherlandshassetitselfthetaskofhavinghalved itsprimary energy consumption per unit of production atthe end of the century, compared to 1980.As a result, a large number of energy-saving measures have been suggested to meet this target. In this book a simulation model ispresented that can be used as atool tojudge the measures proposed. The model describes the dynamics of the greenhouse climate, the components of the heating system and the greenhouse climate controller with a time resolution of up to 1 minute. Also, the photosynthetic activity ofthecanopy isdescribed. Consequently themodeltakes account for the complicated horticultural practice. The simulation model isconstructed from sub-models. Eachofthese sub-models is discussed in detail. The sub-models for the heating circuit, the condenser and the short-term heat storage facility were newly developed. Therefore, theseparts ofthemodel arediscussed extensively.The greenhouseclimatecontrollerandthe greenhouse climate simulation are described integrally, however briefly, because these parts of the model are a reflection of the current state-of-the-art. Toproofthequalityofthesimulationmodel,computations arecomparedtomeasurements on arose crop in aresearch facility. These comparisons aremadeboth with a high resolution on a small time scale (10 minutes) and with aggregated values on a large time scale (year round daily results). Toanalyzetheprospectsofenergy-savingmeasures ingreenhousecultivation,the simulation model was applied to nine energy-saving options. The results of the model onthese options with respect to energy consumption andbiomass production are compared with a reference situation. The reference situation comprised a customary greenhouse growing tomatoes in the Netherlands. From the options evaluated, the application of combined heat and power and alternative cladding materials appeared toyieldthe largest decrement of specific energy consumption (the energy consumption corrected for production effects).  Key words: Energy saving, greenhouse climate simulation, heat storage, climate control, heating systems  CONTENTS  Contents 1. Introduction and organization of the thesis 2. Energy-saving options for horticulture in the Netherlands 2.1 Energy consumption and production in horticulture 2.2 Options that contribute to energy saving 2.2.1 Improvements of heating system engineering 2.2.2 Improvements of the greenhouse building 2.2.3 Energy conserving heating devices 3. A simulation model as atool to analyze energy-conserving techniques IS 3.1 Introduction 3.2 Model requirements 3.3 Model building  1 1 5 6 10 11 12 12  15 16 19  4. The greenhouse heating system 23 4.1 Introduction 23 4.2 A customary greenhouse climate controller 24 4.3 Basicstructure of amodern greenhouse heating system 27 4.4 Models for heating system devices 29 4.4.1 The heating circuit 29 4.4.1.1 Model description 30 4.4.1.2 Results with the model 32 4.4.1.3 Conclusions 37 4.4.1.4 Connection between the heating circuit model and the greenhouseclimate simulation model 37 4.4.2 Main supply pipe and gathering pipe 38 4.4.3 Boiler 38 4.4.4 Condenser 41 4.4.4.1 Model description 41 4.4.4.2 Results 45 4.4.5 Combined Heat and Power 46 4.4.6 Short term heat storage facility 47 4.4.6.1 Model description 48 4.4.6.2 Results 53 4.4.6.3 Conclusions 56 4.4.7 Expansion system 57  4.5 Assembling the heating device models 58 4.5.1 Model assumptions 58 4.5.2 Computations 59 4.5.2.1 Flows to the heating circuits and the gathering pipe temperature 60 4.5.2.2 Charging flow to the storage tank 61 4.5.2.3 Discharging the storage tank 61 4.5.3 Results 63 5. Greenhouse climate simulation 5.1 Introduction 5.2 Notational conventions 5.2.1 State variables 5.2.2 Fluxes 5.2.3 Exchange coefficients 5.2.4 Exogenous variables 5.2.5 Other variables 5.3 The carbon dioxide sub-model 5.3.1 Structure of the carbon dioxide model 5.3.2 Fluxes in the carbon dioxide model 5.3.2.1 Exchange processes 5.3.2.2 Forced fluxes 5.4 The water vapour sub-model 5.4.1 Structure of the water vapour model 5.4.2 Fluxes in the water vapour model 5.5 The thermal sub-model 5.5.1 Structure of the thermal model 5.5.2 Fluxes in the thermal model 5.5.2.1 Convective heat fluxes Heat fluxes at the surfaces Ventilation Air exchange through the screen 5.5.2.2 Conductive heat fluxes 5.5.2.3 Radiative heat fluxes 5.5.2.4 Forced fluxes Short-wave radiation Latent heat fluxes Sensible heat loss from luminaries  67 67 67 67 68 68 68 69 70 70 70 72 72 73 73 73 75 78 78 84 84 84 87 89 92 93 99 99 103 103  6. Results 105 6.1 Introduction 105 6.2 Comparisons between simulation model and measurements 105 6.2.1 Experimental set-up 106 6.2.2 Detailed comparisons 108 6.2.4 Comparisons for a year round period 118 6.2.4 Conclusions on the model evaluation 120 6.3 Evaluation of energy saving techniques 121 6.3.1 Requested greenhouse climate conditions for the growing of a tomato crop 121 6.3.2 Geometry of a large commercial greenhouse 122 6.3.3 Weather data 123 6.3.4 Energy saving prospectives 125 6.3.4.1 Simple improvements of the heating system 125 Insulation of the boiler 125 Insulation of transport pipes 127 Connection of the expansion vessel 131 Conclusions 133 6.3.4.2 Improvement of the building 134 Improved air tightness 135 Application of athermal screen 136 Coated cladding material 138 Double glazing 140 141 Polymer coating 141 Conclusions 142 6.3.4.3 Energy conserving heating devices 143 Condenser 144 Short-term heat storage 146 Combined heat and power 154 Conclusions 157 6.3.5 Conclusions on the evaluation of energy-saving prospectives . 159 7. Conclusions and discussion References  165 171  Appendices 175 Appendix A: Convective heat exchange 175 Appendix B:Relation between mass and heat transfer 177 Appendix C: Transmissivity of a greenhouse covering structure 178 C.l Direct transmissivity 178 C.2 Diffusive transmissivity 190 Appendix D:Light absorbtion by a canopy stand 192 D.l Model description 192 D.2 Results with the model 193 D.2.1 Absorbtion of short-wave and long-wave radiation in a canopy stand 194 D.2.2 Radiation profile within a canopy stand 196 Appendix E: Long-wave radiation 201 Appendix F: Estimation of the sky temperature 204 Appendix G: Gaussian integration 206 Appendix H: Approximation of saturated vapour pressure 208 Appendix I: Photosynthesis 210 1.1C0 2 fixation in a canopy leaf 210 1.2From leaf assimilation rate to canopy photosynthesis 211 Appendix J: Solar elevation and azimuth 215 Appendix K:Notation 216 Summary  219  ,. Samenvatting  226  Curriculum vitae  233  Dankwoord  235  Introductionand organization of the thesis 1. INTRODUCTION AND ORGANIZATION OF THE THESIS During recent decades,the quantity per unit of growth area and quality of greenhousevegetableand flower production intheNetherlands hasincreased considerably Comparing statistical information on horticulture from 1977with data from 1991showsanincrease inthenumber of cutroses (Motrea)from200to 320per m2 per year and an increase in tomato production from 23 to 46 kg per m2 per year (Vademecum voor de Glastuinbouw, 1978;Kwantitative informatie, 1992). These highproduction figures canbeattributed tothe intensive andwellthoughtout conditioning of the canopy's growing environment, comprising temperature, humidity,radiation,C02-supply andnutrient solution.Other important factors are theincreased levelofeducationamongst growersandimprovements inthegenetic properties of theplants.Also the mean length of the growth season has been increased. Parallel to increments inproduction levels,theprimary energy consumption (the consumption of gas and oil) has also increased. Currently, horticultural boilers account for about 5%of the fossil fuel consumption intheNetherlands (Novem, 1994). Chapter 2presents a brief outline of these recent developments. Due to growing public and governmental concern about the effect of increasing carbon dioxide concentrations in the atmosphere, effort is being made in many sectors of economy to reduce the consumption of fossil fuels. In 1992, in an official agreementwiththegovernment, glasshousehorticulture intheNetherlands set itself thetask of halvingits energy consumption per unitofproduction bythe endofthemillennium,compared to 1980.Toreachthistarget,astrategy hasbeen formulated that includes extension work, education on energy saving techniques andresearch.Asaresult,researchers and companies haveoffered alarge number of suggestions to this end. For most ofthese suggestions the energy-saving effects of the techniques inisolated, well-defined situations can be determined accurately. However, the performance ofthesetechniques inthepractical horticultural situation ismuch more difficult toestimate.Thisisbecausetheoveralleffects ofimprovements ondetails ofthe greenhouse system are related to the duration and intensity of application. Moreover, ingeneraltheapplicationofacombination ofenergy-savingtechniques willresult inlesssavingthanasimplemultiplication oftheindividual effects. For both reasons, the effects of strategies on energy saving can only bejudged inthe context of horticultural practice. Horticultural practice canbetaken intoaccountbystudyingtheeffects ofenergysaving techniques in anumber of operational greenhouses where some do apply theconsideredtechniquesandothersdonot.However,thesefull-scale experiments are expensive and difficult toperform, mainly because it ishard to formulate an experimental set-upinwhichthesubject ofresearch canbeconsidered astheonly  Introduction andorganization of thethesis independentvariable.Small-scale research inspecialist facilities, whichisanother wayofconductingsuchasurvey,canovercome mostoftheseproblems,butitappears to be difficult to generalize the results to horticultural practice. Moreover, animportant problem for full-scale aswell assmall-scale experiments istheyear round time span during which the effects must be studied. In addition, locational andyearlyvariation oftheweathertowhichagreenhouse isexposed confuses the observation of empirical research objects. Because of these difficulties there isaneed for amethod tojudge energy-saving techniques inthecontextof complicated horticultural practice inan unambiguous and reconstructible way. Therefore, this work presents a simulation model intendingtomeetthisneed.Withthismodel alargenumber ofenergy-savingoptions is analyzed. Withrespect toenergy saving,attention hasbeen focused ontheheatingofgreenhouses, since heating isresponsible for 95%of the horticultural energy demand (Novem, 1994).The energy-saving options can be divided into three categories, namely theefficient production and handling ofheat, methods toreduce theheat demand of greenhouses and measures to enhance production capacity. The efficient production ofheat involves the application of a condenser, the use ofwasteheat from public electricity production plants andthe application ofonsitecombinedheat andpower units.Handlingofheatinvolves theheatingsystem lay-out andthe application of short-term heat storage. Developments to decrease theheatdemand of greenhouses include improvements intheinsulation ofgreenhouses, such as the application of alternative cladding materials and the use of thermal screens. Another important contribution to reducing theheat demand of a greenhouse is the formulation of a greenhouse climate which combines ahigh production levelwithalowenergy demand (Bakker, 1994;Rijsdijk, 1993).Here, thedevelopment ofnewclimatecontrol strategiesisofmajor importance (Henten, 1995). The simulation model used tool to study energy-saving options is described in Chapter 3,4 and 5.InChapter 3the functional demands onthemodel are defined and the modelling technique isselected. It isshown that the energy consumption of a greenhouse istheproduct of the interaction between the greenhouse climate controller, the heating system and the greenhouse climate in conjunction with environmental conditions and horticultural requirements. Ofthethree components ofthemodel, the greenhouse heating system hasnotyet been a subject of detailed study. Therefore, the formulation and application of sub-models for heating system devices is a substantial element in this work and ispresented inChapter 4.After discussingthe individual elements, an integration ofthe sub-models intoacoherent heating system model ispresented. Finally,the heating system simulation is coupled to the greenhouse climate simulation by means ofthegreenhouse climate controller. Despitetherecent scientific develop-  Introduction andorganization of the thesis ments in greenhouse climate controllers (Hashimoto e.a., 1993), in the present work(theessenceof) acommercially availablecontroller isapplied.Thishasbeen donetostay closetothecurrent practical situation. The functional description of this climate controller is presented in Chapter 4. The components of the model describing the greenhouse climate are discussed briefly but integrally inChapter 5.Thediscussion isbrief becausethispartofthe model has a state-of-the-art character. Obviously, a model can only be an approach to reality. Therefore, prior to the application ofthemodel for theanalysis ofthevarious energy-saving options,the quality ofthemodel isstudied bycomparing oftheresultsofthemodel computationswithmeasurements takeninanactual greenhouse.Thispart oftheresultsof this work ispresented in Section 6.2. After the quality of the simulation model has been proved, a large number of energy-saving options are evaluated in relation to a reference situation (Section 6.3). Thereference situation wasanaverage greenhouse growingtomatoes inthe Netherlands. Finally, the conclusions of the study are presented and discussed in Chapter 7.  Energysavingoptionsfor dutch horticulture 2. ENERGY-SAVING OPTIONS FOR HORTICULTURE IN THE NETHERLANDS Glasshouse horticulture makes an important contribution to economy in the Netherlands. Production accounts for about 5%of gross domestic product(CBS, 1994b).About 76%ofproduction isexported. In 1992thisrepresented avalueof NLG 16.3-109,which was about 6.6% of total export value. Ontheotherhand,modern glasshousehorticulture isanenergy-intensive economic activity. In 1992, about 10%of the domestic gas-consumption (equivalent to 5% of domestic primary energy consumption) was used in horticultural boilers. Becauseofwidepublic concern abouttheglobaleffects ofthecombustion of fossil fuels, the government aims to stimulate all sectors in economy toreduce their fossil fuel use. In this context, the government of the Netherlands has made an agreement with representatives of horticulture to make an effort in the direction ofenergy conservation. Thetarget formulated intheagreement, henceforth referred to by the MJA (Meerjarenafspraak), is to cut the economically normalized specific energyconsumption (ENSEC) measured by 1980standardsbyhalfbythe endofthemillennium (Meerjarenafspraak, 1992).IntheMJAanumberofmeasures to achieve this target are proposed. TheMJAalsocontains adefinition ofENSEC. Basically theENSEC isadimensionless figure representing the outcome of the division of an annual primary energy consumption by an economic value oftheproduction that it generated, as a percentage to the outcome of the same expression with data holding for 1980. Theenergyconsumption iscorrected for deviatingweather conditionsandtheproduction is corrected for inflation. In a formula: E Prim,act  production,9 8 0 r , ,«, n ENSEC = 100 —+—H —~ [-1 (2.1) production.^ Eprim]980 Byexpressing theproduction usingthe economic value oftheproduce,thequantity can be computed for every mix of horticultural products. In Section 2.1 the target of the MJA is explained and discussed within the context of the developments of energy consumption and production in the period 1980 to 1993. From thedefinition ofENSEC wecanseethat itsvalue canbedecreased bothby a decrement of primary energy consumption and by an increment of theproduction. However, the majority of the measures mentioned in the MJA concern energy-saving techniques,rather than techniques that enhance production. Therefore, this study concentrates on technical improvements only. In Section 2.2 the optionsmentioned intheMJAarediscussedbriefly. Fromtheseoptions,anumber have been selected and evaluated in this study. CMQCr  lftft  Energy-saving optionsfor horticulture inthe Netherlands 2.1 ENERGY CONSUMPTIONAND PRODUCTION IN HORTICULTURE  TheDLOAgricultural EconomicsResearchInstitute(LEI-DLO)periodicallypublishes areport onthe developments of the horticultural sector with special reference to energy consumption (Velden, 1993;Velden, 1995). The results of these reports are based on questionnaires distributed amongst 300 nurseries, of which a 100produce vegetables, 100produce flowers and 100produce pot-plants. The companies are selected unbiased and are considered to be representative for the sector. All data mentioned and displayed graphically in this section are derived from these periodic reports. From the data presented by LEI-DLO, the course of the ENSEC for three subsectors and the aggregated mean value could be deduced. These results are presented in Figure 2.1,together with the objective formulated in the MJA.  Economically normalyzed specific energy consumption vegetables flowers mean  1980  1985  1990  1995  2000  year  Figure2.1 Courseof theENSECduringtheperiod 1980 upto 1993.The dotted straightlineshowstheobjective tohave been reachedbytheendofthe millennium. InFigure 2.1 it isremarkable that, inrecent years,themean value oftheENSEC isveryclosetothecurve for flowers andpot-plantsandseemshardlytobe affected by the higher values for vegetables. This is a result of the weighing of the contribution of each of the horticultural sub-sectors in the final figure according to their relative production value. Thus, the course of the partial ENSEC for flowers and pot-plants, having high economic values, despite the comparable growth area (see Fig. 2.2), has a larger impact on the mean ENSEC than the course of the partial ENSEC for vegetables. The fact that in 1992 all partial ENSEC's are larger or equal to the mean ENSEC is assumed to be caused by a  Energyconsumption andproduction in horticulture lowpartialENSECofplantbreederies, forwhichnodetaileddatawerepublished. Figure 2.1 shows that in the early 1980s a vast decrease in ENSEC has been achieved.After, say 1986,thistendencychangesintoaslightincrement. Together withtheever increasingarea (seeFig.2.2),horticulture intheNetherlands shows a gradual increment inprimary energy consumption towards 139PJ in 1993(see Fig. 2.3). Glasscovered area [103ha]  1985  1990  2000 year  Figure2.2 Glasscoveredarea With respect to the absolute energy consumption of horticulture in the Netherlands,theMJAcitesthegeneralgovernmental objectivetoreducetheC02-exhaust ofeach economic sector to 96%oftheC02-exhaust ofthat sector in 1990bythe end ofthemillennium. BecausetheC02-exhaust ispractically linearly dependent onprimary energy consumption, theC02-exhaust objective canbetranslated into atarget fortheabsoluteenergyconsumption intheyear2000.Thistarget(111PJ) is indicated with an arrow in Figure2.3. Assaid,adecrement ofENSEC canbeachievedbyadecrement inprimary energyconsumption (thenominator) oranincrement ofproduction value(thedenominator). In Figure 2.4,the course of thevalue of horticultural products per unitof area, indexedto 1980,isshown. The figure showsa steady increment ofproductionvalue,althoughtheslopeseemstohaveflatten somewhat inrecentyears.Part of the increment of production can be attributed to developments in glasshouse equipment such asthe application ofarockwool rooting medium andthegradual replacement of old, relatively dark greenhouses, by new buildings with a higher transparency for solar radiation.  Energy-saving options for horticulture in the Netherlands  Primairy energy consumption [PJ year']  1980  1985  1990  1995  2000  year  Figure 2.3 Primary energy consumption of horticulture in the Netherlands  Production [NLGm'year']  pot-plants  > weighed mean vegetables  1980  1985  1990  1995  2000  year  Figure 2.4 Course of horticultural production per m2greenhouse in 1980 guilders. Courses of individual products are weighed according to their contribution to the total economic value of horticultural products. However, after observing Figure 2.1, it must be concluded that most production enhancement must be related to energy consuming modifications, such as C 0 2 supply with exhaust gases and artificial illumination. Indeed, Figure 2.5 shows that, in the period 1988 - 1993 the mean primary energy consumption per unit of greenhouse surface tends to increase by 0.05 GJm"2year"' per year.  Energy consumption and production in horticulture Extrapolating the production value per m2 (Fig. 2.4) and the primary energy consumption per m2 (Fig. 2.5) to the values marked with an arrow, the ENSEC will be 72 at the end of the millennium. Obviously, in order to reach the target of the MJA, a serious change in current trends must be realized. Against the background of the flattening curve in Figure 2.4 and the causal relation that seems to exist between increment of production and increment of primary energy consumption, it is more likely that the necessary decrement of ENSEC can be achieved by changing the trend of Figure 2.5 than changing the production value per unit of greenhouse surface. Assuming that the decrement of energy consumption per m2 greenhouse can be achieved by technical measures that donot affect production, an ENSEC of 50 can be achieved when the mean primary energy consumption per m2 greenhouse isdecreased to 1.15 GJm2year"'. A possible path to that value is shown by the dashed line in Figure 2.5.  Primary energy consumption[GJm2year']  1980  198S  1990  1995  2000  year  Figure 2.5 Mean primary energy consumption per m2greenhouse. The dotted line follows the trend of recent years. The dashed line is apossible curve that brings the ENSEC to 50 in the year 2000 if the production value were to develop according to the dashed line shown in Figure 2.4. When the glass covered area in the year 2000 has grown to 11-103 ha in the year 2000 (the dotted line in Figure 2.2), and assuming a mean primary energy consumption of 1.15 GJm2year"' (the dotted line in Figure 2.5), the absolute yearly energy consumption in horticulture will be 126 PJ. This is more than the target cited in the MJA (111 PJ). If the ENSEC is brought back to the agreed value by means of enhancing the production value (increasing the denominator instead of decreasing the nominator in Eqn. 2.1) the violation of the objective with respect  Energy-saving optionsfor horticulture inthe Netherlands totheabsoluteleveloftheenergyconsumptioninhorticulturewouldbecomeeven more severe.Therefore, the measures proposed in the MJAto decreaseENSEC aimatthedecrement ofenergy consumptionratherthantheincrementofproduction. In Section 2.2 these measures are presented in more detail.  2.2 OPTIONSTHAT CONTRIBUTETO ENERGYSAVING  Having read Section 2.1, it is obvious that, in order to reach the target of the MJA,thereisagreatneednecessitytodecreaseenergyconsumptioninglasshouse production.IntheMJAastrategyhasbeenformulated toachievethisdecrement. The strategy is based on extension work, education on energy-saving techniques andresearch.Thedocument presentsalargenumber of energy-savingmeasures, which are subdivided into six clusters. The first five clusters are arranged in a sequential level of applicability. The sixth cluster consists of measures inwhich organizational and management problems dominatethetechnical issue.Thesuggestions are listed in Table 2.1 Table 2.1Measuresproposed bytheMJA (Meerjarenafspraak) tosaveprimary energy. Cluster 1.  2. 3.  4. 5.  6.  10  Proposed measurements a. Condenser b. Boiler insulation c. Attachment of the expansion tank d. Location of the heating pipes e. Decrement of leakage f. Insulation of transport pipes g. Boiler control h. Climate controller a. Overhead screens b. Screens along gables a. Heat storage b. C0 2 supply with pure C0 2 c. Distribution circuit volume a. Heat pump b. Alternative cladding materials a. Geothermal energy b. Long-term heat storage c. Wind turbines d. Application of Biogas e. Low energy demanding greenhouses f. (Semi)closed greenhouses g. CCystorage a. Waste heat at low temperature level (about 60 °C) b. Reject heat at high temperature level (about 90 °C) c. Combined heat and power  Optionsthatcontribute toenergy saving In all activities in the field of extension work and education on energy-saving techniques,theenergy-saving prospects andthecosts associated with implementation arethetwocentral points of interest. Such information, combined with economic constraints,enablesgrowersandextensionworkerstoselectappropriate measures. Asfaraseconomic quantities areconcerned, avast amount of information isreadily available(Kwantitatieve Informatie, 1994).However, gathering dataontheenergyconservingprospectsoftheproposed optionsismuchmoredifficult. The major problem with energy-saving techniques that saving potentials are dependent onthehorticultural context inwhich themeasures areapplied. This difficultyis explained inmore detail inChapter 3.Toovercome this problem,the present study uses a simulation model that serves asa tool toestimate energysavingmeasures inthecontextoftoday's horticulture. Toillustratetheresultsthat can be obtained using this tool, nine of the options mentioned inTable 2.1 are evaluated.Theevaluatedoptionsaregrouped accordingtothreeitems.Theresults of the evaluations arepresented inChapter 6. The first item concerns relatively simple improvements tothe engineering ofthe greenhouseheatingsystem.Thesecond itemconcerns improvements tothegreenhousebuildingandthethirditeminvolvestheapplicationofenergy-savingheating devices. These three items arediscussed briefly below.  2.2.1 Improvements of heating system engineering InTable2.1fivemeasures areproposedthatdealwiththeengineeringoftheheating system (Option lb, lc, Id, If, 3c). Most ofthese measures arestated in the first cluster, meaningthatthey arereadily available.Decrement ofthevolumeof the distribution circuit (Option 3c),which improves the controllability ofthe heating system, meansthereplacement ofall heat distribution loops inaheating circuit and,therefore, it is a major operation (heat distribution loops in aone hectare greenhouse have atotal length ofsome 12km). Thus theapplicationof smallvolumeheatingpipesisonlyan option innurseries thathaveyettobebuilt. The effect ofthe volume of heating pipes hasnotbeen considered inthis study in order tolimit thenumber ofoptionstobediscussed. Of the four remaining options, three options will be evaluated in Chapter 6, namely theinsulationoftheboiler,theinsulationoftransportpipesandtheattachment of the expansion system. Insulation of the boiler andtransport pipes isa relativelysimpleoperation.Theattachment oftheexpansionsystemtotheheating system isexpectedtoaffect energy consumption becauseitaffects themeantemperature ofthe expansion vessel (andtherefore itsenergy loss).  11  Energy-saving optionsfor horticulturein the Netherlands Computations on energy-savings from the alteration of the location of heating pipes are not performed because the present work does not provide sufficient entries to study this effect.  2.2.2 Improvements of the greenhouse building With respect to measures concerning the greenhouse building six options have been identified in Table 2.1 (Option le, 2a, 2b, 4b, 5e and 5f). In Chapter 6 Option le, 2a, 4b and 5ewill be evaluated. Thedecrement ofleakageinvolvesthecareful tuningoftheventilation equipment toensurethatallwindowsareclosedwhenthey aremeant tobeclosed. Overhead screens areconsidered tobeanimportant method indecreasingheat lossfrom the greenhouse cover. Screens in gables (Option 2b) have been left out of this discussion because of the one-dimensional character of the simulation model (see Chapter 3). With respect to alternative cladding materials the energy saving property of a number of options to increase insulation will bestudied. This will be done along the line of yet available techniques. Option 5e is treated in the context of the improvement of greenhouse cladding, sincetheheatlosscanbeconsideredtobeconcentrated aroundthecoveringstructure. Option 5f isnot studiedbecausethethrust ofthisoption isstrongly dependenton new technologies for cooling and dehumidification, which lay far beyond the scope of this work. Contrary to the measures discussed in Section 2.2.1, improved insulation of the greenhousemay haveimplications for biomass production becausetheamount of solarradiationenteringthegreenhousecanbediminished byadditional absorbtion by the covering structure. Therefore, the effect of measures in this item are expressedintermsofspecific energy consumption,defined astheamountofprimary energy consumption per unit of photosynthesis.  2.2.3 Energy conserving heating devices In Chapter 6 three options concerning the application of energy-saving heating devices are discussed, namely the condenser (Option la), the short-term heat storage facility (Option 3a)andthecombined heatandpower engine (Option6c). All these options can be readily applied in nowadays horticulture. The hardware and software that will be assumed to be used with the condenser and the combined heat and power engine will have a negligible effect on the greenhouse climate. Therefore, these devices will not have an effect on biomass 12  Optionsthatcontribute toenergy saving production. However,thisisnotthecaseasfar asaheatstoragetankisconcerned becausetheC0 2 supplyregime and,withittheindoor C0 2 concentration islinked to aheat storage tank. Thus,just asin Section 2.2.2 the energy savings from heat storage arejudged on its effect on specific energy consumption. Again,the implementation ofmeasures from thefifthcluster, such asOption 5a, 5cand 5dare left outof discussion because oftheir experimental character. Heat pumps and the application of reject and waste heat are not discussed either because these heating devices require athorough revision of the heating system in the present generation of greenhouses.  13  Introduction 3. A SIMULATION MODEL AS A TOOL TO ANALYZE ENERGY-CONSERVING TECHNIQUES 3.1 INTRODUCTION  Themostsimpleconceptofamodern greenhousewithrespecttoenergyconsumption isabuildingthat gainsheat from the sunand from combustion of fossil fuels and looses energy to itsenvironment through sensible and latent heat release.Of these energy inputs,only the consumption ofprimary fuels (oil, natural gas etc.) are generally considered as energy consumption. Therefore, energy conservation isjudged on its impact on fossil fuel input only.Energy-saving techniques affect theenergyhouseholdbyenlargingthecontribution ofsolarradiation intheenergy input, improvingtheconversion efficiency betweenprimary fuels andusableheat or by achieving a decrement of energy losses. Theabsolute,andoften eventherelativeeffect ofmeasurestosavefossil fuels are related to the level of energy demand. This energy demand is a highly dynamic quantity duetothediurnal variations inweather conditionsoutsidetheglasshouse and, to a lesser extent, variations in the required indoor climate. Therefore, to study theimpact of energy-conserving techniques,the dynamic characteristics of energy demand onwhichthesetechniques actmustbeavailable.Generally, these characteristics involvemore than one factor. Acondenser, for example, increases the conversion efficiency of a boiler as a function of two variables, namely the current heating power of the boiler and the temperature of the water fed to the condenser.Anotherexample istheapplication ofthermal screens,whichsavesignificantly more in a greenhouse with a young crop than in a greenhouse with a mature crop,because inthelatter thescreen isquiteoften opened tosome extent to carry off moisture. Especially the last example demonstrates that the potentials of energy saving techniques must be studied within the context of a greenhouse. In this work, this context is created artificially by means of a simulation model. The model describes primary energy demand, as a function of the required indoor climate and outside weather conditions. To realize the required indoor climate the model includesagreenhouseclimate controller. Itscharacteristics andthatofthebuilding, the canopy and the heating and ventilation systems are taken into account. The application ofasimulation model enables afast andreproducible analysisof theeffect ofvariousenergy-saving strategiesonayearround base.Inthischapter therequirements onthemodel are formulated. Moreover, theapproach chosento build such a model is presented.  15  A simulation modelas atool 3.2 MODEL REQUIREMENTS  The consumption of primary energy in greenhouses takes place in the heating devices that comprise the heating system. The heating devices considered inthis workareaboiler, aheatstoragetank,acondenser andacombinedheatandpower engine(CHPengine).TheboilerandtheCHPengineareassumed toapplynatural gasastheprimary energy source.The heatstorage tank delaysthe application of heatproduced earlier bytheboiler ortheCHPengine andthecondenser produces heatfrom exhaustgases.Thusaheatstoragetankandacondenser donotconsume primary energy. Therefore they have an indirect effect on energy consumption only. The performance of the heating devices, especially the condenser the heat storagetank,dependsonoperatingconditions,suchastherequired heatingpower, therequired supply temperature and thetemperature of thewater returning from the heating circuits. Therequired heatingpower andsupplytemperature aredetermined bythe greenhouseclimatecontroller.Therefore, theformulation ofthedemandsonthesimulation model begins with the requirements of the climate controller. Climate controller actions are based on acomparison between the desired conditions of the greenhouse air (temperature, humidity and C0 2 concentration) and actual values. Thus theactual values of the greenhouse air conditions have tobe described bythesimulation model.Thedesired conditionsaredefined bycontroller setpoints. Because the greenhouse climate controller is part of a closed-loop process (except illumination control), the simulation model has to describe the impact of controller actions such asheatingpower and carbon dioxide supplyon its feed-back quantities. Feed-back quantities for customary greenhouse climate controllers are the greenhouse air temperature, humidity and C0 2 concentration andthetemperatures oftheupper and lower heating circuit. When a storagetank isavailable,thetemperatures atthetopandbottom of thetank aretwo additional important quantities.Consequently,allthesequantitieshavetobedescribed bythe state variables of the model. In line with the decision to begin the description of the demands on the model with the climate controller, the state variables that serve as an input variable for theclimate controller arereferred toasprimary statevariables.Thecourse ofthe primary state variables is not determined by controller actions only, but are also aresultofinteractionswiththeenvironment ofthephysicalobjectstheyrepresent. The environment includesother objects, represented by other statevariables (definedassecondary statevariables)andtheoutsideweather conditions.Thecourse ofsecondarystatevariablesaffect thegreenhouseclimatecontroller's actionsonly indirectly. Among the secondary state variables in the greenhouse, the canopy temperature is the most important because it has a considerable impact on transpiration and photosynthesis (Stanghellini, 1987;Gijzen, 1992).Photosynthesis affects the C0 2 16  Model requirements concentration, andtranspiration hasanimportant impact onhumidity andtheheat demand of the greenhouse. The temperatures of the greenhouse cover, floor and soil are the next important secondary statevariables.Thecovertemperature determinestheextentofconvectiveandradiativelossesattheroof.Moreover, incaseitstemperature isbelowthe dewpoint, condensation occurs,resulting inadehumidification ofthegreenhouse air. The soil temperature has aconsiderable influence onthe greenhouse climate on days with large fluctuations in temperature and solar radiation level because itcanaccumulate andrelease largeamounts ofheat.Tobeabletodescribe atemperature gradient, the soil has to be split into a number of layers (Bot, 1983; Houter, 1989; Takakura, 1990). The top layer of the soil is referred to as the floor. The energy losses at theroof are significantly diminished bythe application ofa thermal screen.Becausetheclosed screen actsasashieldtothermal radiation, the temperature of the screen is an important quantity. Moreover, a closed screen separates the greenhouse air intotwocompartments. Therefore, by the definition ofthreestatevariables for theairabovethescreen,thetemperature, humidity and C0 2 concentration of the air above the closed screen is distinguished from the temperature, humidity and C0 2 concentration of the air below the screen. If the greenhouse is equipped with a heat storage tank another set of secondary statevariables hastobedistinguished, namely thetemperature ofthewater strata between thetop and bottom of the storage tank. During charge and discharge of the tank these strata shift downward and upward respectively. In Figure 3.1,all state variables are depicted in closed frames. The open frames refer totheexogenousstatevariables (see below).Theprimary statevariables are accentuated bybold frames. Theframeofthestatevariable representing thethermal screen's temperature is extended to improve readability of the picture. The notational conventions with respect to the naming of variables are presented in Sections 5.2.1, 5.2.4 and 5.2.5. Besides by actionsofthe greenhouse controller, conditions inthe greenhouse are severely affected bytheexogenousstatevariablesrepresentingtheoutsideairand skytemperature andtheoutsidehumidity andC0 2 concentration. Theair andsky temperature affect the convective and radiative heat losses at the greenhouse cover. The sky temperature is defined as the black body temperature of the sky vault,representing thethermal radiation from theatmosphere according to Stefan Boltzman(seeappendixE).Outsideairtemperature,humidity andC0 2 concentration have implications for the indoor climate conditions by air exchange through opened windows and cracks. Solar radiation isan important exogenous flux variable sincethe sun isthe most important heat source of a greenhouse. Moreover, the sun is essential for photosynthesisandimportant withrespecttocanopytranspiration. Because greenhouse 17  A simulation modelas atool transmissivity andphotosyntheticactivitydiffer significantly fordirectand diffuse radiation, the solar radiation data have to describe both quantities. The third meteorological quantity required for the simulation model iswind speed because of its impact on ventilation and heat losses from the cover.  Windsp  T,  1 TfflO!  C02al  "-fr  VP  st02  ™M3  JTio  TJ greenhouse  ™*>i  storagetank  Figure3.1 Graphic representation of thestatevariablesinthemodel. During the night, the variations of outside weather conditions and the indoor climate are relatively small. Thus the controller output and performance of the heating devices isquiteconstant, which allows asimulation model that generates data on greenhouse conditions with hourly intervals or even larger. However, sometimebefore sunrise, andduringthedaytime, greenhouse climate conditions canchange quicklydueto setpoint changes, opening ofthethermal screen,variations in solar radiation and ventilation. As a result the controller output also changesfrequently. Thus,tokeepupwiththedynamicsofrealgreenhouseclimate controllers, the interval for simulated data on greenhouse air conditions must be in the order of minutes. Sincemanyweatherdatasetsarepresented inhourlyaverages,themodel samples theweather datawith at onehourly intervals, However, toprevent large stepwise 18  Model requirements changes from one hour to the next, the meteorological data between the hourly means are approximated by linear interpolation. Finally, because alterations tothe greenhouse building, itsheatingdevices and its control mayhaveimplications for canopy growth,themodelrequiresthedescription of biomass production.  3.3 MODEL BUILDING  The development of simulation models can be considered two follow oneoftwo routes (Palm, 1986).Oneroute istofindarelation between the input and output of a system solely by observing the input and output data. This is called system identification andthe model generated isoften referred to asa black-box model. This technique is employed successfully in control engineering applications. In greenhouse climate modelling theblack-box approach was adopted by Udinkten Cate(1983) for instance. In general, theparameters inthistype of model havea limited physical interpretation and haveto bedetermined in an experimental setup. Thesecondroute istosplitupthesystemtobemodelled intoanumberofsmaller subsystemswhosepropertiesarewellknownfrom previousexperience,andtofollow this with an appropriate interconnection (Ljung, 1987). This modelling approach isbased onthecomputation of thelevel of astatevariable inapart ofthe system from thenetflux totheconsidered part. The energy content ofsuch apart is governed by an energy balance according to "  W  [Js 0 ](3.1)  If the state variable concerns a mass content, its rate of change is governed by a mass balance reading: ! T = <t>net,m  [kg^] (3.2)  In general terms a net flux is defined by: 4>net= E 4>i„ " E < U + E production  [a.u.s"'] (3.3)  The production term, which is generally important in models for chemical reactions, is zero in all net flux computations stated in this work. The fluxes <t>ni and <j)out are either forced fluxes (e.g. an electric heater) or fluxes that result from a potentialdifference betweentheconsidered partofthesystemanditsenvironment (e.g. a temperature difference between a heating pipe and air). By definition, forced fluxes havean imposed magnitude.Fluxesthat result from apotential difference are determined by a flux equation. 19  A simulationmodelasatool For heat transport (j)net isexpressed inW.The flux equationbetween two discrete physical entities reads: 4>E= G (Ta - Tb)  [W] (3.4) 1  withGaconductivity (WK" )andTa-Tb(K)thetemperature difference thatserves as a potential difference. The conductivity can be a function of the temperature difference. When Tarefers to thephysical entity of interest and Tbto atemperatureofanentityofitsenvironment Eqn. 3.4 describes anoutward flux (otherwise Eqn. 3.4 describes an inward flux). Ta can be either a boundary variable or the temperature of other modelled entities. Thenetheat flux toaphysical entityinducesatemperature changerate according to  Ul  n  1  AT  Jt  <E G i( T " T i) + E Production)  VWT v  c  [Ks"1](3.5)  i=l  P p  withVthevolume(m3),pthedensity (kgm*3)andcpthespecific thermal capacity (Jkg"'K"')oftheentity,nisthenumber ofdistinguished fluxes from otherentities. The notation of Eqn. 3.5 with T at the right hand side of the equation and dT/dt at the left hand side stresses that the differential equation can be solved by forward integration.Thedenominator oftherighthandsideofEqn.3.5isreferred to as the capacity of the state variable. For masstransport <|)ne, isexpressed inkgs"1.The flux equation for masstransport relates the flux to a concentration difference. In general terms itreads: [kgs"1](3.6)  4>m= k (ca - cb)  with k a mass transfer coefficient (mV1) and ca-cb(K) the concentration difference.Thenetmass fluxtoadistinguished volume inducesaconcentration change rate according to dc 1 n Ht= v ( £ k i( c " c i) + 2 production) u  [ k g m V ] (3.7)  i=l  with V thevolume (m3) of the entity. As in Eqn. 3.5, n isthe number of distinguished fluxes from other entities. In the present model, state variables that are governedbymassbalancesareexpressed asapartialpressure.However,aconcentration can be expressed as a partial pressure quite easily by application of the ideal gas law. Doing so, Eqn. 3.7 turns into: n  HP R T (  *  It Mr .? k i (p - p i }+ £ P roduction )  [pas''] (3-8)  with Rtheuniversal gasconstant (8314Jkmor'K'1) and Tthetemperature ofthe volume (K),Mthe molar massoftheconstituent of interest (kgkmol"1) andVthe dimension of the volume (m3). k*is an exchange coefficient that relates a mass 20  Model building fluxto partial pressure difference. The integrals ofEqns.3.5 and 3.7or3.8 describethecourse ofthestatevariables over time. For simple systems, when the fluxes depend linearly on thevaluesof thestatevariables,theintegral canbesolved analytically.However, whenmodels become abit more complex, as is certainly the case with the model discussed in this work, the equations are solved with a numerical integration scheme (e.g. Euler-integration). Themajor advantageoftheconstruction ofmodelsbycombiningpreviousexperienceovertheblack-boxmodel, isthephysicalmeaningofthevariables andintermediate results in a model developed along the second route. Because these quantities (fluxes, temperatures and pressures) can be interpreted physically, adaptions of the greenhouse system in order to decrease its energy consumption can be studied by modifying small parts to the model. ThesecondrouteofmodelbuildingwasemployedbyBot&vanDixhoorn (1978) in order to build a detailed and validated greenhouse climate simulation model. From general theory onheatandmasstransport, they assembled amodel thatdescribed the course of temperature and humidity in a greenhouse as a function of pipe-temperature, solar radiation, ventilation and outside weather. An important part of the simulation model presented in this work is an elaboration on their model. Since the late seventies, scientific progress in the field of greenhouse climate modelshasbeenachieved byimproving thedescription oftheheatexchangeprocessesinthegreenhouse.Goudriaan(1977)developedimpressivetoolstocompute theabsorbtion ofbothlong-wave andshort-wave radiationwithin acanopy stand. Bot (1983) was the first to present a complete greenhouse climate simulation modelthatcouldreadily beimplemented onacomputer. Heextensively described the ventilation process, light transmission and convective heat exchange at the greenhouse cladding and convective heat exchangeprocesses between the greenhouse air, the heating pipes, the canopy and the soil. In addition he made afirst start to the computation of the transpiration of a canopy. Stanghellini (1987) provided asounder base for the description of canopy transpiration, in particular for a tomato stand. Balemans (1989) described heat and mass exchange at and through thermal screens.DeJong(1991)contributed considerably tothedescription and computation of the ventilation process through windows. Manyothershaveconstructed greenhouseclimate simulation modelsbycompositions,andmostly small modifications orsimplifications, ofthework ascompared to the previously mentioned authors (Takakura, 1992;Houter, 1989; Jolliet and Bailey, 1991). Withthetheoriespresented in literature,the greenhouse climatepart ofthesimulation model could be assembled. The description of the state-of-the-art greenhouse climate simulation model that emerged ispresented in Chapter 5. 21  A simulationmodelasatool Contrary tothemassive attention intheliterature onthemodelling of greenhouse climate, little attention hasbeen given to the dynamics oftheheating system and the description of the interaction between devices in that system. Therefore an important part ofthis study isdevotedtothedefinition of models for elementsin the heating system. Attention is also paid to the connection between these elements asthey form an integrated system. The heating system model is presented in Chapter 4.  / 22  Introduction  4. T H EGREENHOUSE HEATING SYSTEM 4.1 INTRODUCTION  A greenhouse heating system consists ofdevices forheat production and heat dissipation. The devices fordissipation of heat, like pipes filled with hot water orhot air blowers, serve tocreate a favourable micro-climate around the canopy. When heat isdissipated from hotwater pipes, thewater isheated byoneor more heat production devices. Hot air blowers combine dissipation and heat production. However, because of the relatively small importance of these devices in today horticulture, hotairblowers arenotdiscussed here. In Chapter 3itwas argued that the relation between theprimary energy consumption of heat production devices and the heat produced depends on the duration and the conditions inwhich the devices areoperated. Both factors areaffected by the greenhouse climate controller andthegreenhouse climate produced. In turn,the heating devices affect thegreenhouse climate. To structure this chain ofprocesses, thegreenhouse climate controller is considered to be theinitiator of heating system performance. The interactions ofthe greenhouse climate controller with the heating system and the greenhouse climate is schematized inFigure4.1  return temperature heating system |' simulation 3 pipe temperature C0 2 supply  CHP control exhaust gases supply pipe temperature setpoint  artificial lighting window aperture  1  tr^rrr-rBWEr«sBiiri^..»^*Tg  greenhouse climate simulation U  air temperature humidity C0 2 concentration  global radiation outside air temperature  Figure 4.1Aschematic representation of thegreenhouse climate controller initiating control actions on the heating system and thegreenhouse. The greenhouse climate controller reacts togreenhouse air conditions. 23  The greenhouseheating system Because of the central role assigned to the greenhouse climate controller, this chapter begins with a description of its functionality. The control actions imply the heating system, the control of ventilators, artificial illumination, carbon dioxidesupplyandthermalscreens.Temperature, humidityandC0 2 concentration control require feed-back quantities to be compared to setpoints. The feed-back quantities aretobeobtained from thegreenhouse climate,whichlinkstheclimate controller to the greenhouse climate simulation model. The greenhouse climate simulation model is discussed in Chapter 5. The relation between control actions on the heating system and primary energy consumption isdetermined bythecharacteristics ofindividual devicesintheheating system in conjunction with each other. Therefore, after discussing the greenhouse climate controller, the structure of a modern greenhouse heating system is displayed.Thisisfollowed byapresentation ofmodelsthatdescribethebehaviour of the constituting devices.  4.2 A CUSTOMARY GREENHOUSE CLIMATE CONTROLLER  Oneofthereasons for theimportant improvements thathavetakenplaceinhorticultural production duringthelast decades isthewidespread introduction ofintegrated greenhouse climate controllers. A greenhouse climate controller attempts to realize a requested set of greenhouse air conditions by means of adjusting heating, ventilation and C0 2 supply. Also, it is quite common that the climate controller affects theamountofshort-waveradiation inthegreenhousewithshading screens (to decrease the amount of light) and artificial lighting (to increase radiation levels). Inthiswork, shading screens are not discussed because principally they arenotrelatedtoenergy consumption, although theshadingscreen can be used as a thermal screen with very poor energy saving characteristics. The determination of actual values for temperature, humidity and C0 2 setpoints can be situated at the top of the functional hierarchy of a climate controller. In general these setpoints are aresult of settings obtained from theuser interface, in combination withthetime ofday andthemeasurement ofmeteorological quantities.For example,thesetpoint for the greenhouse airtemperature isparametrized by a day and night temperature setpoint, aslopeto increase the setpoint from the nightvaluetothedayvalue,aslopetobringthesetpointback from thedaytothe night value and a 'light dependenttemperature setpoint increment'. The lightdependent temperature setpoint increment constitutes a linear relation between the temperature setpoint and solar radiation. It isparametrized bythe tangent of the relation, athreshold on which to start the increment and amaximum increment. Humidity setpoints are commonly defined by a daytime and a nighttime value only.The climate controller ofthepresent model takesaccount for allparametrizations mentioned above. 24  A customarygreenhouse climate controller Tocontrolthecarbon dioxide concentration, aclimatecontroller suppliesC0 2 by means of astrategy related tothe maximal supply rate,rather than by realizing a C0 2 setpoint. In fact theparametrization concerns a maximal C0 2 concentration and amaximal supply rate. In modern controllers, the supply rate isgoverned by algorithms that take account of thepresence of aheat storage facility. However, the greenhouse climate controller in the present model confines with the first mentioned, simple C0 2 supply strategy. The on-off control of artificial illumination is based on the comparison of the actual intensity of global radiation with a setpoint. Besides the control based on outsideradiation, for apresetperiodduringthenight, illumination isswitched off. Moreover, illumination is commonly not applied between May and August. Thesecond leveloffunctionality comprises thecomputation ofrequested window apertures and the determination of pipe temperature setpoints. Windows in a greenhouse can beopened either for dehumidification or to cool the greenhouse. Thus, infact thewindowaperture isdetermined bytwocontrollers.Inthepresent model, both are implemented byproportional controllers. The controller for temperature opensthewindow only when the temperature exceeds the setpoint bya certain extent (e.g. 1 °C).Atemperature excess abovethis dead zone implies an openingaccordingtoaparticularproportionalband.Thehumiditycontrolleropens thewindowatanangleproportional totherelativeexcesscompared toahumidity setpoint.Thefinalwindowaperture isthemaximum oftheapertures requestedby the controllers. Thewindowcontrollerfirstopenstheleesideventilators.Whenthecomputedwindow aperture exceedsaparticular deflection (e.g. 30°),the controller onthe leesidewindowsbecomessaturated.Thenthewindward sidewindowsareopenedas well. In fact, inthe model, the control of the windward side windows is similar to the control of leeside windows but with a dead zone of 7°C. The heatingpipe controller computes arequested pipe temperature excess onthe greenhouse air temperature setpoint with a (digital) Pi-controller. In the first instance,thecontroller outputisassignedtotheprimary heatingcircuit. However, when thistemperature exceeds athreshold, which isdefined intheuser interface, thesecondary heatingcircuit startstoaccompany theprimary heatingcircuit.The excess of the requested temperature on this threshold is assigned partly to the primary and partly to the secondary circuit. Apart from thetemperature controller, apreset minimum pipetemperature affects the requested pipe temperature. A minimum pipe temperature is defined in the user interface and iscommonly set atsome40to 50 °C.In general the requested minimum pipe temperature during the night differs from the minimum pipe temperature setpoint for the day.Moreover, during the day,when the intensity of outside global radiation exceeds athreshold (e.g. 100Wm"2)the setpoint for the minimum pipetemperature isdecreased linearontheexcess.Inthepresentmodel 25  The greenhouse heating system therateofdecreaseissuchthattheminimum pipetemperature equalstheairtemperature setpoint when the solar radiation is 300 Wm"2.The pipe temperature to berealizedisthemaximum oftheminimumpipetemperature andthetempearture computed by greenhouse air temperature controller. The third level of hierarchy in a greenhouse climate controller is constituted by mixing valve controllers. The mixing valve controllers adjust the valve position when the temperature of the water deviates from the setpoint passed from the heating pipe controller. Commonly the temperature of the water after mixing is measured just behind the valve.  26  Basicstructure ofa modern greenhouse heating system 4.3 BASIC STRUCTURE OF A MODERN GREENHOUSE HEATING SYSTEM  Inthisstudy,theterm heatingsystem refers toasetofdevicesfor theproduction, transport anddissipation ofheat.Thesimplest heatingsystem consistsofaboiler, transport pipes and one or more heating circuits. In Figure 4.2 a sketch of such a heating system is presented. To strain different agglomerates in the heating systemtheboiler isdrawn inaboilerhouse,which isconnected tothe greenhouse by a transport pipe. The heating circuits are located in the greenhouse, which is the other agglomerate.  Figure4.2A simplegreenhouse heating system. By controlling the boiler mixing valve,the temperature inthe transport pipe can bekeptafew degreeshigherthanthehighesttemperature requested intheheating circuits. The temperature of the water in the heating circuits is controlled by a mixing valve on each circuit. Inrecent years,the simple concept shown in Figure 4.2 has evolved into amuch more complicated system, which includes acondenser, a heat storage tank anda combined heat and power engine (CHP engine). The condenser was introduced after thefirstenergy crisis intheearly seventies.The introduction ofheat storage tanks was coupled to the application of C0 2 from exhaust gases from the boiler andbeganinthemid-eighties(Vermeulen, 1987).Suchastoragetankaccumulates heat surpluses when the boiler combusts gas in order to produce C0 2 during periodswhenthere isno(orlimited)heatdemand.Accumulated heatcanbewithdrawn during periods of heavy heat demand. The application of CHP engines began in the late eighties. First these engines appear on nurseries that applied artificial illumination in order to produce their own electricity. Nowadays the majority of CHP engines in horticulture produce electricity for the public grid (CBS, 1994a). 27  Thegreenhouseheating system The addition ofthesecomponents totheheatingsystem implied serious adaptions ofthe boiler house. Both theboiler and CHP engine haveto be connected to the heat storage tank and the condenser requires a second transport pipe from the boilerhousetothegreenhouse.Thissecondtransport pipebringsthereturn water from thecoldestheatingcircuittothecondenser. Whenthissecondtransport pipe is omitted the condenser is fed from the return side of the transport pipe, at a temperature close to the return temperature of the hottest heating circuit. Such a high temperature affects the efficiency of the condenser negatively. Anexample of aheating system made upof thedevicesmentioned above ispresented in Figure 4.3  Figure4.3A heatingsystem withaboiler, acondenser, combinedheatandpower anda short-termheatstoragefacility. Figure 4.3 makes clear that the CHP engine is treated in the same way as the boiler. The heating circuit connected to the condenser also has a connection with thetransport pipe from the boiler (and CHP and heat storage tank). This facility enables a supply of additional power to this heating circuit if the heating power of the condenser is insufficient. Each of the devices in the heating system as shown in Figure 4.3 has it's own peculiarities. In the next section, models for the various elements are proposed.  28  Modelsfor heatingsystem devices 4.4 MODELS FOR HEATING SYSTEM DEVICES  4.4.1 The heating circuit A greenhouse heating circuit consists of amain supply and return pipe,towhich a largenumber ofparallel heat distribution loopsareconnected.A sketch ofsuch a heating circuit ispresented in Figure 4.4. The valve determines the mixing ratio between hot water supplied to the circuit andcooledwaterreturning from thedistributionloops.Thusthemixingvalveenables the climate controller to realize a pipe temperature in the heating circuit, lowerthanthetemperature ofthewater fed tothevalve.Thevalve isabletorealize any mixing ratio, although in general the relation between thevalve position and mixing ratio is non-linear, especially near the extreme positions. The circulation pump ensures a(more or less) constant flow through the heating circuitry, irrespective ofthepositionofthemixingvalve.Commonly thecapacity ofthe circulation pump issuch that thevelocity inthedistribution loops isabout 0.08 ms"1. mixingvalve   circulation pump  ^ M ^  - f e  transport section •-  transport section  distribution loop  Figure4.4A greenhouse heatingcircuitwith circulationpump andmixingvalve. "3m3 per A heating circuit contains a substantial amount of water (about 2.5-10 m2 greenhouse) and, therefore, has a large heat capacity. Moreover, due to the structure oftheheatingcircuit, andthecapacity ofthecirculation pump,thetimelag between a temperature change at the main supply pipe and a new stationary situation at the main return pipe is in the order of twenty minutes. Because the 29  The greenhouseheating system temperature of a heating circuit has to rise and fall frequently, the capacity and time lagoftheheatingcircuitry hasbeen taken intoaccount inthepresentmodel. Most of thepiping network isdesigned to serve both asaheattransport ductand aheatingsurface. Part ofthepipingisinsulated andhasatransport function only. In this section, a model isdescribed that determines the temperature distribution alongtheheating circuit asafunction ofthetemperature atthesupply sideofthe circuit, taking intoaccount the dynamics of the system. The model description is followed by a comparison of the model with measurements.  4.4.1.1Modeldescription The starting point of the model description is the concept of a piece of heating pipe, filled with moving water. On the outer side, the pipe releases heat to its environment andontheinnersidethepipeisheatedbythewater flowing through the pipe. This conceptualization is depicted in Figure 4.5.  Figure4.5A sectionofa heatdistribution looploosingheattothe environment andgainingheatform waterflowing throughthepipe. Ifthevelocity ofthewaterinthepipeisabout 0.08 ms'1 andassuming aninternal diameter of0.047 m,theReynolds number isabout 6-103.Therefore itisallowed toneglect aradial temperature gradient. Moreover, because theresistance toheat transport from theouterpipe surface totheair isfar greater thantheresistanceto heat transport from the inner to the outer surface of thepiping material (a factor 100)itisallowedtostatethatthetemperature ofthepipesurface equalsthewater temperature. With the assumptions stated above the general differential equation that describes the temperature of an infinitesimal length dxreads: 5T„;,  5t  30  m  8T T + V C = clTr, cap K i p ^ p i p W p i p " air) P PKetT7 )  [Ks"'] (4.1)  Modelsfor heatingsystem devices ThefirsttermbetweenthebracketsofEqn.4.1takesaccountoftheheatexchange between thepipeandtheenvironment. Thethermal capacity ofthepipe slicecap iscomputed from thelumpedcapacityofwaterandpipingmaterial.apipisacombined heatexchangecoefficient ofconvectiveheatexchangebetweenpipeandair and radiative heat exchange between the pipe and the opaque bodies around the pipe.ppip is the perimeter of thepipe. The second term in Eqn. 4.1 contributes for the net inflow of energy into the infinitesimal pipe slice.Thisterm includes the velocity of the water v(ms"1), the volumetric heatcapacity of water pcp (Jm"3K"'), thewet surface of the pipe slice Awet and the axial temperature gradient 5T/8x. Inthepresent model, alldifferential equationsare solved numerically. Therefore, both the axial gradient and the infinitesimal time step dt must be assigned to a finite length andtime respectively. Bymaking the length of apipe segment such that thevolume of the segment equalsthevolume ofthe water displaced through thepipewithin thefinite step intimeboth discretizations areparametrized bythe discrete time step only. With the time step denoted bytsthe length of a discrete pipe segment is defined by: Iseg= •£*-  M (4.2)  Denoting the temperature of a particular pipe segment Tpipjand the temperature oftheadjacent pipesegment upstream Tpipi.„ thediscretization ofEqn.4.1yields: dT  pip.i dt  v c A  P P wet(Tpip,i-t-Tpip,i) - a pipWpip( T pip,i- T air) Cap s e g  [Ks-1](4.3)  The thermal capacity of a pipe segment is computed by: Cap S e g = H* lSeg ( d in 2 ^  ^  +  3.6340 6 (d o u t 2 - d jn 2 ))  [JIC1] (4.4)  where 4.18-106 and 3.63-106 are the volumetric thermal capacities of water and steel respectively (JK' m'). Numerical integration of Eqn. 4.3yieldsthecourse ofthe temperature ofapipe-segment intime.Application ofthe Euler-algorithm withthepreviously mentioned time step tsyields:  In case the heat loss of a pipe segment isnegligible and the heat capacity of the pipingmaterial issmall compared totheheatcapacity ofthewater inthepipe,as is the case with the wide insulated main supply and return pipes in greenhouses it can be shown that Eqn 4.5 turns into a simple shift-register algorithm of the form Tpip/t+ts) =Tpip)i.,(t). 31  The greenhouse heating system 4.4.1.2Results with the model Totestthemodel,measurements werecarried outontheoverhead heatingcircuit ofasmallgreenhouseresearch accommodation of200m2(seealsoSection 6.2.1). Asketchoftheheatingcircuit ofthisresearch facility isdepicted inFig.4.6.The dimensions of the sketch are not to scale.  circulation pump  I, ©  W~ KD isaa Figure 4.6 A sketch of the heat distributioncircuit applied to test the heating circuitmodel.Thelocationof thetemperature sensorsis indicated. Intheexperimenteighttemperature sensors(thermocouple, K-type)wereattached onthepipeandwrappedwithinsulatingmaterial.Thesensorswerescannedevery ten seconds by a datataker 500 data-acquisition device. Thefirstpartoftheheatingsystem,whichran from thefirstsensortothesecond, is a 12meter steel pipe with an inner diameter of 41 mm and an outer diameter of 45 mm. With a capacity of the circulation pump being 3.3-10"4mV 1 thetime lagof thispart ofthe distribution system is 52seconds. Thus,with a 10seconds integration step (chosen to be equal to the sample interval of the measurements) five segments were used to represent the first part. The remaining two seconds wereneglected. Since most ofthis section inthe distribution system is insulated, theheat loss component wasapplied tothe last segment only.Thetemperature at the first sensor is modelled by the temperature of the first segment. The second section of the distributing system isa 28.5 meter pipe with a 47mm inner diameter and a 51 mm outer diameter. This pipe section spans from the second sensor upto the attachment of theheat distribution loop.The time-lag in 32  Modelsfor heatingsystem devices thispartofthesystem is 178seconds,resulting in 18 model segments.Thetemperature at the second sensor isrepresented by the first segment of this part of the model. Thethird section is formed bythe heatdistribution loop,which is44meter long. AscanbeseeninFig.4.6theheatdistribution loopwiththesensorsisthesecond of four loops.The pipe has an inner diameter of 25mm, and when it is assumed that the water is divided equally over the heat distribution loops the time-lag in thethird section is282seconds(28segments).Thetemperature atthe3rd,4thand 5th sensor is described by the 2nd, 14th and 27th segment of this section of the model respectively. The fourth section, built from the same piping material as the second, spanned 31.5meters.This section wasmodelled by 20 segments.The lastsegment ofthis model-section represents the temperature at the sixth sensor. Thefinalsection,whichran from thesixthsensortothemixingvalve,is 17 meter longandisassembled from thesamepipesasthefirstsection.Thusitisdescribed by a 7 segments model-section. Because the major part of this pipe is insulated, only the first two sections contribute to a heat loss component. Intheexperiment, boththedynamic effects ofasudden openingofthevalveand thecoolingdownprocessafter themixingvalveisclosedhavebeenobserved.The observation of the first effect was carried out after the valve has been closed for a long period of time to ensure that all water in the distribution circuit had the sametemperature.Theresultsofthemeasurements andthesimulatedtemperatures are depicted in Figure 4.7. Duetothespecific characteristics oftheheatingsystemoftheexperimental greenhousethesupplywater atthemixingvalve(measured with sensor 8anddepicted with the dashed curve) took about 2 minutes to reach a temperature close to its final value.Moreover, duringthetime spanoftherest oftheexperiment itshowed a slow further increase. Because the supply water temperature at the mixing valve didnotrisestepwise,inthesimulation themeasured supply water temperature was treated as an input variable. Figure 4.7 shows that the measured and simulated temperatures for Sensor 1were very close to the dashed line. Indeed this must be expected because practically all return water from the distribution circuit is refreshed when the mixing valve is opened. Besidesthesupplywatertemperature,theheatexchangecoefficient apipisanother inputfactor inthesimulation model.From convectiveandradiativeheatexchange theory, presented in Appendix A and Appendix E, an overall heat exchange coefficient wasfitted asafunction oftemperature difference betweenpipeandair temperature, assumingthattheradiativeenvironment oftheheatingpipeconcerns black elements at a temperature T^. The best fit for the overall heat exchange coefficient for temperature differences in a range between 1and 60 °C for the three types of heating pipes appeared tobe: 33  Thegreenhouseheating system a = 6.8(T pip -T air ) 018 1stand 5th section (45 mm) a = 6.7(Tpip-Tair)0-18 2nd and 4th section (51 mm) a = 7.2(T pip -T ajr ) 018 3rdsection (28 mm)  [Wra-2K-'] (4.6a) [Wm-2K-'] (4.6b) [Wm-2K-'] (4.6c)  IntheseequationsT j refers tothemeanpipetemperature ofasection.Theexponent for thecombinedradiativeandconvectiveheatexchangecoefficient issomewhat lower than the 0.25 that holds for a convective heat exchange coefficient solely because, for small temperature differences, theexchange coefficient ofthe radiative part in the heat exchange process is fairly constant (exponent zero). In order to improve the match, for the comparisons between measurements and simulation theconstant 6.7 in Eqn. 4.6b was incremented to 7.5 and the constant 7.2 in Eqn. 4.6c was enlarged to 8.0. An explanation for these higher values is that a number of assemblies were attached tothese pipe sections (taps, chains to hang it in the greenhouse). Temperature [°C]  24 30 time [minutes]  Figure 4.7 Temperatures at sevenpoints in a distributioncircuit half anhour after a stepwise opening of the mixing valve of the circuit. The numbersrefer to Fig. 4.6. (••• = measured, = simulated, =temperatureofsupplywater, measuredwithsensornumber8). Ingeneral Fig.4.7showsagoodsimilarity between measurements andsimulation, except for theseventh sensor. However, theconsiderablefinaltemperature difference between the measured temperatures at Sensor 6 and 7 give rise to doubts about the signal of the seventh sensor. It is very unlikely that 17 meter pipe, 34  Modelsfor heatingsystem devices which isinsulated for a large part, gives atemperature decrement comparable to the decrement of a more than thirty meters non-insulated and wider pipe in the fourth section of the distribution circuit. Therefore in the following no value is attributed to the level of the seventh sensor, but only to its dynamics. Themajor difference betweenmeasurement andmodel occurs inthedynamicsof thetemperature at the 6th and 7thsensor. Contrary to themeasurements the slope ofthesimulated temperatures atthe6th and7thissimilar to theslope ofthe other curves. The slope of the measured temperature curves for these last two sensors issignificantly lessthan the slopeofthe other curves.Aplausible reason for this discrepancy is the model assumption that the time for a water sample to travel through the circuit is equal irrespective of the distribution loopthrough which it travels,whereasinarealcircuitslightlydifferent hydraulicresistancescausesmall velocitydifferences inthedistribution loops.Sincethemainreturn pipemixesthe waterfrom four distribution loopsthedifferences intravellingtimes inducealess steep temperature rise. Measurement andsimulation ofthecoolingdownoftheheatingcircuitareshown in Figures 4.8 and 4.9.  Temperature [°C]  -i—i—i—i—i—r-1—<~~'—i—'—i  •  i—'—i—'—i—'—r  5 10 15 20 25 30 35 40 45 50 55 60 time [minutes] Figure4.8Measured(• • ) andsimulated( afterclosingthemixing valve.  ) temperature atthefirstsensor  35  Thegreenhouseheating system  Temperature [°C] 9U  (D  807060-  l7TtT.N.  _  50  ^ — - " ' ^  •,•". I ' . X ^ ,  40< '  , "T—i  1  r  | "i  1  1  1—'"I—  1  1  '  1—'—l—l—1—1—(—1- - 1 — I — 1 — 1 — 1 — 1 —  0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 time [minutes] Figure 4.9 Temperatures at the third, fourth andfifth sensor after closingthe mixingvalve (• •• =measured, =simulated). Again, the simulation is in fair agreement with the measurements. However, in Fig. 4.8 it can be seen that the simulated temperature drops are slightly steeper than the measured curve. The slow decrease of the measured temperature at the first sensor,just atthebeginningoftheprocess isprobablycaused by somecapacitive effects of the attachment of the sensor to the pipe. Theotherlesssteepslopesofmeasuredtemperature decrementsthanthesimulated curves can be contributed to the same effect that caused the slower temperature rise at the 6th and 7th sensor as discussed above. The fact that in this graph the measured and simulated temperatures atthefirstsensor showa good match after a fewminutes,givesfurther reason for doubtingthemeasured temperatures atthe 7th sensor (see discussion on Fig. 4.7). because, after closing the valve, the temperatures at the seventh and first sensor are in fact about equal (apart from a small time-lag). InFigure 4.9 itcanbeclearly seenthat ittakesabout 4minutes before the effects of changes at the mixing valve occur at the beginning of the heat distribution loop.  36  Modelsfor heatingsystem devices 4.4.1.3 Conclusions From acomparison oftheresults ofsimulation and measurement, asdiscussedin theprevioussection,itcanbeconcludedthattheproposedmodel indeeddescribes thedynamicsofthetypeofheatdistribution systemscommonly appliednowadays in horticulture. Moreover the results show that the cooling down curve of a distribution circuit doesnot yield asmoothly decreasing return temperature buta series of rather fast temperature decrements succeeded by rather longperiods of constanttemperature.However,inacommercial greenhouse,wherenormallymore than some 50 distribution loops are attached to a single main supply and return pipethiseffect willbemuch lesspronounced because quiteimportant differences in travelling times through the distribution loops will are likely.  4.4.1.4Connection betweenthe heating circuitmodel and the greenhouse climatesimulation model Asstated inChapter 3,the greenhouse climate simulation model takesaccountof asinglestatevariable for boththeupperandlowerheatingpipe,whereastheheating circuit model applies some 50state variables per heating circuit. To connect bothapproaches,thepipetemperature applied for aheatingpipeinthegreenhouse climate simulation model is the mean of the pipe segment temperatures in the distribution loop section of the heating circuit model. Another complication is the heat exchange coefficient at the distribution loops (apip), which has to be a lumped convective and radiative heat exchange coefficient in the present model, whereas, aswill appear in Chapter 5,the greenhouse climate simulation model separates the heat release in a convective and several radiative heattransfer processes. Thisproblem issolved bythe computation ofa heat exchange coefficient at each simulation step from the sum of all heat losses from theheating pipe,ascomputed bythe greenhouse climate simulation model, andtheactualtemperature difference betweenthemeanpipe temperature andthe air temperature. As a formula this approach reads: ii  «„;„ = , ,T ^ ' TS ^i [Wm-2K-'] (4.7) P'P (mgfl«(T pip )-T air )l pip p pip where the operator meanrefers to a function computing the mean value of the temperatures of the pipe segments.  37  The greenhouseheating system 4.4.2 Main supply pipe and gathering pipe Themain supply pipe(see Fig.4.3) collects hot water from the devicesthatproduce heat and transports this water to the mixing valves of the heating circuits. Thegatheringpipebringsthewaterback from theheatingcircuits totheheatproducing devices. In this study, in order to be in line with the tendency in present dayhorticulture,theflow throughthemainsupplypipe,andconsequentlythrough the gathering pipe as well, is assumed to be variable. The volume-perimeter ratio of transport pipes is comparable to, or even larger then, that of the main supply and return pipes, discussed in the former section. Moreover thepipes arecommonly insulated. Thus, ifthepipes are long,thetime lag induced can be described by a simple shift register (see Section 4.4.1.1). However, in most greenhouses the mixing valves of the heating circuits are concentrated in the boiler house. Consequently, the model presented in this work omits atime-lag in the distributing pipes.  4.4.3 Boiler Boilers applied in horticulture are devices with aheating capacity that ranges up to about 7.5 MW. Typically the installed heating capacity is 250 Wm"2 greenhouse. The boilers are constructed from a horizontal cylindric vessel filled with waterinwhich alargecombustion chamber andanumber oftubesconductinghot combustion gases are situated (see Fig.4.10).  a boilerfromtheoutside  combustion gases combustion chamber a boilerfromtheinside Figure4.10Sketchofa horticultural boiler. 38  Modelsfor heatingsystem devices The combustion gasesflowfromthecombustion chamber totherear sideofthe boiler. Then thegases maketheir waytothefrontoftheboiler through some10 to 20pipes. Atthefront, thedirection offlow isagain reversed. Thefluegases flowbackward through another setofpipes. Finally thegases leavetheboilerto the chimney or,ifpresent, tothecondenser. Due totheheavy construction and large amount of water in the boiler (inthe order of 10m3foraboiler inaonehectare nursery) theboiler represents amassive heat capacity. However, since thetemperature ofthe water intheboiler is kept (about) constant (90 °C), with respect tothepfresent model thecapacityof the boiler isof little interest. Commonly, asingle loop controller onthetemperature ofthewater intheboiler adjusts thepower oftheheater intheboiler. Byadjusting the flow from theboiler tothetransport pipe,thedevice canproduce anyheating power requested. For a short timetheboiler caneven supply morepowerthanthemaximal powerofthe heater. Apart from theproduction of heat, the boiler can be used to generate C0 2 to enrich thegreenhouse airwith carbon dioxide.Toensure theproduction of C0 2 whenthere isaneedforC0 2 supply,theheatingpoweroftheboiler canbebounded toaminimal value. To limit theheat losses atthesurface ofthe boiler, theboiler is insulated with rockwool and covered with thin PVCor aluminum plates. With insulation,the total resistance toheat transport ofthe boiler wall isaseries oftwo resistances, namely thethermal resistance oftherockwool andthe surface resistance toheat transport ofthe boiler covering. Thus, theoverall heat exchange coefficient for heat loss from theboiler surface, being thereciprocal ofthe total resistance,is defined by: "boiler = (  1/a  insu + ^ s u r f ) " 1  [ W i ^ K " 1 ] (4.8)  In Eqn.4.8theresistances of the insulation material andtheboiler surface are expressed bythereciprocal ofthe heat exchange coefficients. For theinsulation material, theheat exchange coefficient canbe found inhandbooks.Forrockwool avalueainsu=0.04/dinsuwasfound (polytechnisch zakboekje 1987), with dinsuthethickness ofthe insulation (m). The heat lossatthe surface results from thesumofradiative andconvectiveheat exchange.Boththeseexchangemechanisms areanon-linear function oftemperaturedifference betweensurface andenvironment (seeAppendicesAandE). Since the surface temperature depends onthethermal resistance ofthe boiler wall,the heat lossatthesurface has tobedetermined byaniterative procedure. Theresult ofthisprocedure fortheheatexchange coefficient ofaboiler withwaterat90°C to an environment at 20 °C as a function of insulation thickness is shown in Figure 4.11.Thediameter oftheboiler (thecharacteristic dimension forthecom39  The greenhouse heating system putation of the convective heat loss) was assumed to be 2.3 m and the emission coefficient of the aluminum covering was assumed to be0.3. To illustrate that the overall heat exchange coefficient above a certain insulation thickness isgoverned bytheinsulation,theheatexchange coefficient ofrockwool isshownasadashed line.Obviously,whentheinsulationthicknessexceeds5cm, the overall heat exchange coefficient is governed completely by the thermal resistance of the insulation material. Heat exchange coefficient [Wm!K'] 12 _. heat exchange coefficient ofinsulation  totalheat exchange coefficient  6 8 10 insulation thickness [cm] Figure 4.11 Heat exchange coefficient of a boiler with water at 90 °C to an environmentat20 °Casafunctionofinsulation thickness (fullcurve). The dashedcurveshowstheheatexchange coefficientofthe rockwool insulation solely.  40  Modelsfor heatingsystem devices AAA Condenser A condenser exploits the latent heat present in the exhaust gases of a boiler or a combined heat andpower engine.Thus,the heatingpower of acondenser isprimarily governedbytheamount andcomposition ofexhaustgases.However, since a condenser is a heat exchanger, the second determining factor for the heating power is the temperature of the water entering the condenser. This is because condensation occurs onlywhenthetemperature of theheatexchanging surface is belowthedewpointoftheexhaustgases.Thisdewpointissome60°C (Meijndert, 1983). In horticultural practice a distinction ismade between a 'single condenser' anda 'combi condenser'. A singlecondenser has only oneheat exchanging circuit and acombicondenser hastwo.Inacombicondenser theheatextractionfromtheexhaust gases isperformed intwo stages.The first stage ismeant to cool the gases toatemperature ofabout 80°C,whereas inthesecond stagethegases arecooled totemperatures belowthedewpoint.In asingle condenser theentire coolingprocess is performed in the one heat exchanger. The major reason for using a combi condenser rather than a single condenser is that the first enablesto connect the first stage of the device tothe gathering pipe (seeFig.4.3).For thistypeofcondenser, onlythesecond stageofthedevicehas tobeconnectedtoalowtemerature heatingcircuit.Thus,partoftheheat gathered by the condenser becomes available at a widely applicable, relatively high temperature. Consequently, theheat release capacity oftheheating circuit applied to carry off thelatentheatof theexhaust gases(gathered inthesecond stage)canbe smaller. In fact, thetypical characteristics of acondenser are concentrated onthe second section of the combi condenser only. Because the high temperature character of the heat gathered in the first section, from modelling point ofview, this section can be considered a part of the boiler. Thus,the second section of a combi condenser can betreated as a single condenser which cools exhaust gases froma boiler with an enhanced conversion efficiency. Thereasoning aboveleadstotheconclusionthat, from themodellingperspective, thesame approach canbetakentoasingleandacombi condenser, providingthat the conversion efficiency of the boiler is treated as a variable. Such a model is presented in the next section. In Section 4.4.4.2 some results obtained with the model are shown.  4.4.4.1Model description Thefirstfactor that affects condenserperformance istheconstitution ofthecombustion gases. From the literature (Gasunie, 1980) it can be calculated that the combustion of 1 m3natural gas(Slochteren quality,at0°Candstandard pressure 41  Thegreenhouse heating system of 101kPa) requires 2.52 kg Oz and produces 1.35 kgwater. Since thecombustionofgasisperformed bytheadditionofoutsideairwhichcontainsabout20.7% oxygen, it can be computed that stoichiometric combustion3 of natural gas requires 11.0kg of outside air. With the density of natural gas,being0.834 kgm"3and Xthe air factor6, thetotal mass flow of the exhaust gases is expressed by: u exh = 0.83 + 11.0 X.  [kgm"3combusted gas] (4.9)  The major components inthe exhaust gases areN2 and 0 2 , which originate from the outside air, and H 2 0 and C0 2 , which are combustion products. Only asmall fraction of the exhaust gases is made up of other gases (Argon, NOx etc). The specific heat capacity of the exhaust gas can be computed from the specific heat of the components, weighed according to their mass ratio in the mixture. J 2 . 0 uH20 + 1.07 nN2 + 0.82 uC02+ 0.92 ii02) 103 Vxh (HH20+ HN2 + HC02+M02>  , , P™ K ] (4.10)  with nmo, uN2, n co2 and u 02 the massofthemajor elements intheexhaust gases after combusting a m3 natural gas and 2.0-103, 1.07-103, 0.82-103 and 0.92-103 thespecific heatcapacitiesofvapour,nitrogen,carbondioxideandoxygenrespectively. The mass of the major elements is stated by: HH2O= 1-35+ 0.08 X  uN2 = 8.20 X Pco2= 1-76 H02 = (*•-1) 2.50  [kgm"3combusted gas](4.11a) [kgm'3combusted gas](4.11b) [kgm'3combusted gas](4.11c) [kgm'3combusted gas] (4.lid)  The term 0.08 Xcontributes to thevapour content ofair led intothe combustion chamber. The value 0.08 isbased on a humidity content of 7 gkg'1, which holds for air of 15°Cand 70%RH. Of course weather conditions will affect theterm, but as the term 0.08 X is already small compared to 1.35, the differences due to outside weather conditions have been neglected. The C0 2 content of outside air hasalsobeenneglected since, for acommon value(340ppm), thisconstitutes no more than about 0.56-10"3kgkg"1. The temperature at which the exhaust gases enter the condenser is dependent on the conversion efficiency of the boiler. To elucidate the heat fluxes, Figure 4.12 presentsaschematicoverviewoftheheatfluxesperm3combusted gasandtemperatures in a boiler-condenser combination. Referring to the boiler efficiency with a variable Tjboi|er, the heat content of the  "Combustion with exactly the required amount of oxygen b  The relative excess of oxygen compared to the amount required for stoichiometric combustion 42  Modelsfor heatingsystem devices exhaust gases at the entrance of the condenser is defined by: Qexh = d " t o i l e r ) 35-16-106  [Jm"3combusted gas] (4.12)  with35.16-106theupperheatingvalueofnatural gas[Jm3].Followingthereasoning set out in the introduction to this section, in the case of a single condenser Tlboji^isintheorderof0.85(Handboek VerwarmingGlastuinbouw, 1995),whereasthe application of a combi condenser can be modelled by increasing rM„(to some figure between 0.87, and 0.89, depending on the size of the first stage) followed by a neglection of the first section of the combi condenser. sensible heat 3  35.16 MJm chemical energy (natural gas)  sensible heat (P^) -T  air  latent heat (Pdhnm) L. boiler  condenser  Figure 4.12 Heatfluxes per m3 combustedgas and temperaturesin a boilercondenser combination. A substantial fraction of the heat content consists of latent heat. The amount of latent heatcan bedetermined easily from the amount ofvapour produced by the combustion process. [Jm"3combusted gas] (4.13)  Q latent = A// uH20  with AHthe heat of evaporation of water (2.45-106Jkg"1). After computation of Qexh and Qlatentthe temperature of the exhaust gases at the outlet of the boiler is defined by: T  =T boiler.out  +• boiler,in  Qexh~Qlatent c p,exh  [K](4.14)  Air for combustion is normally extracted from the air of the boiler house. For convenience,thetemperature ofthisair(T^,^ in)istreated asaconstantof20°C, which is a reasonable temperature for a boiler house. After they have left the boiler, the condenser cools the gases to a temperature 43  The greenhouseheating system whichissomedegreeshigherthanthewaterledtothecondenser.Thetemperature difference between the gases leavingthe condenser and the water fed to the condenserdependsontheengineeringcharacteristics ofthedevice,andthemagnitude of the exhaust gas flow. Within the context of this work there was no detailed information availableonthesecharacteristics. Product information oncondensers showsthat,atmaximal exhaust gas flow, 12°Cisareasonablevalue for thetemperature difference betweenthegasesleavingandthetemperature ofthewater fed to the condenser (van Dijk Heating, 1995).At minimum exhaust gas flow (10% of full capacity),thetemperature difference dropsto3°C.Asafirstapproach the relation between the temperature difference and exhaust gas flow is assumed to be linear dependent to the gas flow. Thus, since the exhaust gas flow depends linearly on the heating power of the boiler, the temperature of the gases leaving the condenser is described by: *cond,out = ^water.in + 2 + "boiler ™boiler,max  t ^J (4-15)  The value P^ie,.isthe actual heating power of the boiler. In case Tcondout is lower than the dew-point of the exhaust gases, the condenser withdrawslatentheatbycondensation.The amountofcondensatecanbecomputedeasilybysubtractingthemoisturecontentofsaturated exhaustairatatemperature Tcondoul from the moisture content of the gases that leave the boiler. The saturated moisture content of the gases leaving the condenser can be determined by a fitted curve. A good approximation of the saturated moisture content of air in the temperature range between 30 and 60 °C was found tobe: x(t) = 1.882-10"313 - 0.1412 t 2 + 5.018 t - 46.57  [gkg'1] (4.16)  The moisture content ofthe gasesthat leave the boiler (and enter the condenser) is determined by: - u - - " d ^ o "  1 0 3  The power added to the heating system by cooling (P^i) (Pdhum) of the exhaust gases can now be expressed as: P  cool= ° ^exhcp,exh(Tboiler,out " Tcond,out)  tete 1<417)  "  an(  * dehumidification t W l (4-* 8 a )  Pdhum= O ^exh0-Xboiler.ou,) 2A5 •l°W C O nd,oJ- x boiler,o»«) [W] (4.18b)  withO thegascombustion rate (m3natural gasper second).Theterm (l-x^^,,,,,) is added because the moisture content is expressed as kg vapour per kg dry air, whereas uexh refers to the mass of humid air. The sum of Eqn. 4.18a and Eqn. 4.18b yields the heating power of the condenser. Pcondenser = Pcool + rnax{0, P d h u m }  44  [W] (4.19)  Modelsfor heatingsystem devices The '/nox'-operator provides that Pdhum iszerowhen thetemperature of the gases leaving the condenser is still above the dewpoint of the boiler exhaust.  4.4.4.2Results The calculation scheme described above was applied to determine the efficiency of a condenser as a function of the temperature fed to the condenser for two air factors (1.2 and 1.4) and for two relative exhaust gas flows (a value 0.2 and a value 0.8 times the maximal capacity). The results are shown in Figure 4.13.In the figure, an efficiency 1means that all heat present in the exhaust gases (sensible and latent) is gained. In the computations the boiler is assumed to have an efficiency of 0.85 with respect to the upper heating value of natural gas.  Condenser efficiency [-] X=1.2  20  30  40  SO 60 70 ingoing water temperature [°C]  Figure4.13 Efficiencyofa condenser as afunction of watertemperaturefed to thedevice,theairratioandtherelativeexhaust gas flow. The figure shows clearly that the condenser efficiency drops rapidly when the temperature of the water fed tothe device increases.However, when the exhaust gasesleavethecondenser atatemperature abovethedewpoint, theefficiency decreases slowly. Figure 4.13 also shows that an increasing air factor reduces the efficiency of the condenser.Thisiscausedbyadecreasingdewpointoftheexhaustgasesfor higher values of the air factor, which can be seen from a combination of Eqn. 4.9 and Eqn. 4.17.  45  Thegreenhouseheating system 4.4.5 Combined Heat and Power Combinedheatandpowerengines(CHP engines)aredesignedtoutilizethewaste heatinherent intheconversion offossil fuels tomechanical energy.Recenthorticulture in theNetherlands shows a rapid increase in the application of these devices. By the end of 1993 CHP engines could be found on 12%of the nurseries (Velden et.al., 1995). The electricity produced by these engines is used on the nursery itself, but more and more of it isbeing fed to thepublic grid. Combinations of private use and supply to the public grid are also customary. Anon-site combined heatandpower deviceused inhorticulture isbasedonapiston engine that runs on natural gas.Nowadays, thetypical thermal power output is about 400 kW per hectare. The typical accompanying electric power is about 250 kW. Figure 4.14 shows the frequency distribution of the installed thermal power of CHP engines in arecent survey on CHP-performance in 28 enterprises (Verhoeven et.al. 1995).  Relative frequency 0.25 0.2  % 0.15 0.1  0  1 w,1'III 1 '///  0.05  7////  '///  'III  $ & ^ tf & tf *? ** ^ & & tf v* Nv> <? $ $> $ ^ $? #? <$? $? & thermal capacity [Wth m-2] Figure4.14Frequencydistribution of thermalcapacityof CHPenginesina representativeset ofgreenhouseswith CHPin the Netherlands. In general the larger engines were installed more recently than the smaller ones. Although theheatingpower output can usually be adjusted, acombined heat and power engine is operated at 100%capacity as much aspossible. This is because the electric efficiency of the engine drops quickly when the shaft power of the enginedecreases.Klimstra (1991)mentions adecrement ofelectricity production to 60%when the heat output isdecreased to 70%of its full- loadvalue. Parallel, the conversion efficiency ofgasto electricity drops form 35%to 30%.Whenthe 46  Modelsfor heatingsystem devices heatoutput isturned downtohalfthefull-load capacity,theelectricity production even drops to only 25%of its maximal value. Then the conversion efficiency of gasto electricity isonly 17%.Toprevent havingtotemper theheating output of theengine,inpracticeeither asmall heatingpower ischosen(<40 W^m"2),orthe engine is coupled to a short-term heat storage tank. As a consequence of thepreference for operating aCHP engine at full-load, this work limitsitselftotreatingtheCHPengineasanon/off heatsource.This simple approach tendstoyield a large number ofengine starts.However, because in all the simulations where CHP is applied a short term heat storage facility is also present, the number of starts and stops remains limited. Since, due to the application of a storage tank the number of starts and stops is small (once ortwiceaday)andtheheatcapacity oftheenginenormalized perm2 greenhouse is small (about 40 JK"'m"2 greenhouse3) in the present model the dynamic behaviour oftheengine isneglected. Thus,when switched on,thecombined heat and power engine is modelled to generate heat instantaneously at a level defined by itsthermal heating power.  4.4.6 Short term heat storage facility The short-term heat storage tanks used in horticulture are commonly horizontal oriented cylindrical vesselswith alargediameter andfilledwithwater. Thewater inthestoragetankcanbeexchangedwiththewater intheheating systemwithout passingheatexchangers.Thevesselsarewellinsulated.About 10cmofrockwool iscustomary. Thedimension ofthesetanksvariesbetweensome 50m3to 150m3. Figure4.15 givesanimpression ofsuchafacility andshowsacrosssectionofthe tank. Duringheataccumulation, hotwater flows intothetankattheupper side,andthe replaces colder water which is sucked from the bottom of the tank. During discharge theprocess isreversed. Bymeansof acareful design ofin- and outstream pipes at the top and bottom of the storage tank the mixing of warm water in the upper part of the tank with cold water in the lower part isprevented as much as possible. On a time scale of the order of some hours, the temperature of the water at the outlet of the storage tank has no relation with the charge or discharge power of thetank.Thismeansthattheinstantaneouspowerthatcanbewithdrawnfromthe storagetankisvery large.Onlywhenthetemperature difference between inletand  "Assuming a temperature difference of 60 °C between the on and off status of aCHP engine,theheatassociated with itsthermal capacity islessthan 1 %o of the daily heat demand. 47  The greenhouse heating system outletissmall,thepower absorption orsupplyisseriously limitedbythemaximal flow to or from the tank. In the following a model is presented, describing the dynamics of horticultural heat storage tanks.  cross-section detail  Figure4.15 A horticultural heatstorage tank.  4.4.6.1 Model description Modellingandcharacterizing heatstoragetanksisanimportant aspectofthetheoretical andexperimental workbeingdoneinrelation todomestic solarheatcollectors. Therefore, a large amount of literature on storage vessel modelling can be found in thisfield. Acentral theme inboth domestic heat storage vessels and the large storagetanks applied in horticulture is the stratification within the vessel. This is because in general a small amount of hot water is more favourable than a larger amount of warm water, providing the heat content is the same. Sincethedensityofwaterdecreaseswithrisingtemperatures (temperatures above 48  Modelsfor heatingsystem devices 4 °C),hotwater tendstofloatoncolder water. However, apart from theconvective charging flow that moves the hot water strata through the vessel, buoyancy flows andconduction induceheattransportfromthewarmtothecoldregion.The relevanceofconductioncomparedtodisplacementduetotheforced charging flow is expressed by the Peclet number (Pe) (Yoo and Pak, 1993) as defined by: Pe = ^  [-] (4.20)  where vis the bulk flow velocity (ms"1), h the height of the tank (m) and a the thermal diffusivity (1.8-10"7m V for water at 55 °C). In a heat storage process characterized by a small Peclet number (e.g. 100) diffusion plays an important role andthetemperature changes from hottocoldover alargeregion. Therefore, the temperature of the cold water at the outlet of the tank already begins to increase when only 60%ofthevolume ofthetank hasbeenreplaced byhotwater. A large Peclet number (e.g. 800) means a steep change from hot to cold. In this way it isnotun till the tank has beenfilledto about 90%that atemperature rise in the water coming out of the tank can be noticed. Duringtheoperation ofaheat storagetank inhorticultural applicationsthePeclet number is commonly high, although not aconstant. It not a constant becausethe chargeanddischarge flows vary intime.Moreover, eveniftheflow werebeconstant, the velocity of displacement of the boundary between hot and cold water would vary with the location of the interface due to the changing width of the (horizontal) cylinder. To get an indication of the Peclet number the bulk flow velocity of an 80 m3storage tank with a diameter of 2.8 m and a length of 13.0 m isdetermined where the charging flow is 10m3 per hour (taken as apractical figure). Whenthe interface between thewarm and cold water is located halfway up the tank the Pe number is at its minimum. From the figures above it can be calculated that the minimal Pe number equals 1.2-103. Kleinbach, Beckman and Klein (1993) presented several types ofnumerical models to describe the dynamics of heat storage vessels. The first type, termed a multinode model, is simple, but neglects the specific property of a stratified storagetank, where hotwaterfloatsoncolderwater. This omission isnotimportant when the Peclet number is small (e.g. 50). However, where the Pe number islarge,themultinodemodelrequires avery largeamount (about 100)of 'nodes' (state variables) to yield steeptemperature changes. Because,this isnotthe case in horticultural practice, as demonstrated above, the multinode model is less suitable. Therefore, in this study, the second model type, termed the plug-flow model is applied. In theplug-flow model, hot packages of water shift upwards or downwards ina conceptual stack, according to adischarge or acharge flow respectively. In fact, the storage tank canbeseen asashift register which isabletoshift intwodirec49  The greenhouseheating system tions. Sooner or later stored packages are extracted from the upper or lower side of the stack. Contrary tothe shift registers for the main supply and return pipe,applied inthe heating circuit model described in Section 4.4.1, the speed with which water is displacedthroughthestoragetankisnotconstant.Assuggested,butnotdescribed, by Kleinbach et.al. (1993), the connection between the shifting process through thestoragetankmodel andtheotherparts oftheheating systemcanbe performed by the definition of an accumulator at the head and tail of the shift register representing thestorage tank. During charging, thetop-accumulator shifts downwardsintothefirstelement oftheshift register, butnotbefore ithasaccumulated thecontinuous flow uptothevolume of ashift register volume.Duringfillingof thetop-accumulator, thebottom-accumulator emptiessimultaneously.Becausethe actual volume of both accumulators together equals thevolume of an element in theshift register, themoment thecontent ofthetop-accumulator isemptied inthe firstelement oftheshift register thecontentofthelastelement canbepushedinto thebottom-accumulator which isempty atthe same moment the top-accumulator is full. When the storage tank is being discharged, the process is reversed. Avisual presentation oftheaccumulator functionality isdepicted inFigure4.15.  top accumulator  bottom accumulator  cell I  celll  celll  cell2  celll  cell2  cell2  cell3  cell2  cell3  cell3  cell 4  cell3  cell4  cell 4  cell4  cell32  cell32  cell33  cell32  cell33  cell33  cell34  cell33  cell34  cell34  cell34  cell32  charging, meaning an increment of the top-accumulator volume  just after a downward shift  Figure 4.16 The shift register representingthe storage tank with its top-and bottom-accumulator. The temperature of the top-accumulator is equal to the temperature of the first element in the shift register. The temperature of the bottom-accumulator equals the temperature of the last element in the shift register. During the filling of an accumulator, it is assumed that the in-flowing water is 50  Models for heating system devices  perfectly mixed with thewater already inthe accumulator (which hasthe temperature of the adjacent compartment. This is acceptable since it is likely that there will be an intensive mixture of water near the inlet. Besides temperature changes due to upward or downward shifting packages of water, temperature changes are induced by convective and conductive heat fluxes between water strata. Moreover, the storage tank looses heat through the wall to the outside air. Especially buoyancy flows, which occur attemperature inversions, induce a fast heat exchange between water strata. Kleinbach et.al. (1993) suggest taking account of buoyancy flows by averaging the temperature of adjacent compartments where the upper one has a lower temperature than the one beneath. To describe these heat exchange processes, besides as elements of ashift register, the cells in the stack are considered as state variables capable to exchange heat with each other and through the wall to the outside air. The conductive heat exchange between compartments is determined by the discrete formulation for heat transfer through continuous media (see Section 5.5.2.2). If the distance between the centres of the first and second compartment is denoted di and the heat exchanging surface is called Aj(see figure 4.17), then the conductive heat loss from an element i to an element i+1 (HStiSti+I) is described by: H  StiSti+i  d{  IW] (4.21)  where X denotes the thermal conductivity of water (0.6 Wm"'K"'). The variable Aj can be computed for the elements in a horizontal cylinder from the angle ©; by Af= 2Ir sin(cOj) (m2), with 1 the length of the storage tank and r the radius of the tank (m). C0jis solved from the equation: •/   /   V  1v  accu.top  (0;- sin((o;)cos((o,) = 7t 1  comp E  *rf  , , ..  —  [-] (4.22)  v  buffer with Vaccu the actual volume of the top-accumulator. The variable d( is determined by dj= r(cos((Oj.,)-cos(coi+1))/2 (m). An example ofthevariables mentioned above for a storage tank represented by a shift register of 8 cells (N=8) is presented in Figure 4.17. Obviously, when the volume of the top-accumulator changes, the angles cOj change. For the first and last compartment the changes ofcohave large effects, for the others the effect is very small. However, in the present model these changes of C0jare neglected. The heat losses to the environment are modelled with a simple coefficient of conductance referred to as G ^ (Wm"2K"'). Denoting the heat exchanging surface S(, where the index i indicates the compartment number, the expression for the heat losses to the environment becomes H  StiOu« = Gtank &i( T sti "  T  ou,)  [W] (4.23) 51  The greenhouseheating system whereToutdenotesthetemperature oftheenvironment ofthetank.Obviouslythe conductance of the insulation of the tank istaken to be constant. This is allowed since the (constant) thermal resistance of the insulation material fairly prevails over the resistance due to the varying outside convective heat exchange. Thevariable Sjcanbecomputed from S;=2(/r(coi+1 -co;)+nrVcomp/Vbuffer) (m2). After computation oftheheatfluxes,thetemperature ofthecompartments atimestep ahead can be determined from: T  Sti(t + t s ) = T sti (t) +  ^Sti-iSti ~  H  c  StiSti+i ~  P p comp  H  StiOut)  [°C] (4.24)  In Eqn. 4.24 ts denotes the step-size. Vcomp isVbufrer/(N+1) for the second up to the lastcompartment butone.Thevolumeofthefirstand lastcompartment isthe same as the others, but incremented with the volume of the top- and bottomaccumulator respectively.  Figure4.17Examplesoftheangleso>/(thedistancesdt thevolumesVcompandthe surfacesAtfor aheatstoragesimulation witheightcompartments. The top-accumulator (andthusthebottom-accumulator) isfilledfor 50%. Compared to the multi-node model, the steepness of temperature changes at the outlet is much less affected by the number of state variables. Where in a multinodemodelanincrement ofthenumberofcellsimpliesanincreasingly steeptemperature gradient, an increment of thenumber of state variables in the plug-flow model only affects the resolution of the temperature gradient (both in time and temperature level).This is because the output of the tank simulation has azeroorder hold character due to the discontinuous shifting process. In this study the number of compartments is set at 34 (meaning that each cell in 52  Modelsfor heatingsystem devices the shift register represents 1/35"1of the storage tank volume. Inthetheory described aboveauniform velocityprofile onthe interface between warm andcoldwaterwasassumed.However, itislikelythatthevelocity atsome parts ofthe interface islarger thanatotherparts.Toincludethis intheplug-flow model,the emptying of the accumulator can be somewhat advanced. This means that an accumulator can be emptied into the shift register when its volume has grown to 90%of theregister cell volume for example. In this case a fraction of thevolumeremains ineachcelloftheshift register (inthiscase 10%)andtherest shifts intothenextcell.This modification yieldsamodel comparable totheheating circuit model, where the piping material represents a thermal capacity that does not displace (see Section 4.4.1).  4.4.6.2Results To check the modelling approach, aheat storage tank in one oftheIMAG-DLO research facilities was charged and discharged. Unlike the storage tanks used in actualhorticulture,thistankwasstandingupright.However,thephysicalphenomena to be checked do not depend on the type of storage tank. Figure 4.18 shows a cross-section of the storage tank used. The volume of thetank was 4m3 and it was insulated with 10cm of rockwool, covered with aluminum plates.  2.30 m  Figure 4.18Cross-section oftheheatstoragefacility appliedto testthesimulationmodel.Thenumbers referto temperature sensors. 53  Thegreenhouse heating system During discharge, the outlet at the upper side of the tank was supplied to the upperheatingcircuit oftheresearch facility. Thecharacteristics ofthiscircuit are described in Section 4.4.1.2.Whencharging, ascanbeseen inthefigure, another setofpipesisusedthanwhendischarge istakingplace.This isanother difference intheparticulartankusedhere,compared tocommonly tanksusedinhorticulture. In the simulations, 20%ofthewater inthe model compartments isnot displaced in order to account for the velocity differences at the interface between cold and hotwater.Thismeansthattheaccumulator isemptiedwhen itreaches 80%ofthe volume of a compartment in the shift register. Thecomparison ofthemodel computations with measurements for a discharging tank which previously has been charged to a temperature of 67 °C is shown in Figure 4.19. Temperature [°C]  14  16 18 time [hours]  Figure4.19Comparison of model-output withmeasurementfor thedischarge of a heat storage tank. The numbers refer to figure 4.18 (•••• = measured, =simulated, = temperature ofsupply water). Except for the first hour for Sensor 3,the model and the simulation agree very well.The discharge process starts att=1.6 hours.This point ismarked by asteep increment inthedashed curve from 23°Ctoabout 34°C.This34°Cistheinitial temperature of thewater returning from the heating circuit that, the moment the discharge begins,flows alongtemperature Sensor 4(see Figure 4.18).Duringthe first hours of the discharge process, the heating circuit is fed with water at a temperature of 68 °C (Sensor Number 5). The circulation pump drives the dis54  Modelsfor heatingsystem devices charge with a flow thatfluctuatesbetween 0.90 and 0.92 m3 per hour (theflow wasmeasured andpassedtothemodel).After about20minutes,thereturntemperature of the heating circuit starts to rise towards 53 °C. This time lag of 20 minutes is larger than the 16minutes that appear in Figure 4.8 because, during discharge of the storage tank, the pumping capacity is a factor 0.8 compared to the experiment subject to Section 4.4.1.2. This decreased flow is caused by an increased hydraulic resistance when thepump doesnot only transports thewater through the heating circuit, but also through the storage tank (and its pipes and valves). Withameanflowof0.91m3perhour,thebendingpoint intheflank oftheoutlet temperature drop is expected to occur 4.4 hours after the start of the discharge process. However, in the picture it appears that this point was reached half an hour earlier. This means that there is quite a lot of so called 'dead space' in the tank. The model has been tuned for this dead spaces by emptying the bottom accumulator in the 33nd cell instead of the 34th. This adaption was performed becausethenozzle on the outlet of thepipe that brings the water intothetank is situated at about 20cm abovethebottom ofthetank. The other reason oftheadvancement ofthebendingpoint isthefraction of 0.2 ofthecompartment volume that is modelled not to shift. The fact that the output of thestorage tank from t=6 hours uptill t=9 hourswas measured (and simulated) tobe49°C andnot the 53°Cthat was supplied tothe tank during thefirsthours ofthe discharge process is surprising. An explanation for this, and which has been included in the model, is that during charging, the storage tank was not completely heated to 67 °C, but that the bottom 50cm remains relatively cold. This assumption is based on the location of the pipe that sucksthewaterfromthetank duringthechargingprocess (seeFigure 4.18).This will be discussed in more detail in the comments on the results of the charging process. Apparently the cold bottom stratum mixes with the supply water during the discharge. However, because this is a special peculiarity of this particular storage tank, no further comments are made on this subject. The results of the comparison between model and measurements for the charge processareshown inFigure4.20.Theagreement ofmeasurements andsimulation for thechargingprocess appearstobegood.The course oftheoutlettemperature matchesparticularly well.Notethat inthefigure, thezero-order hold character of the model output can be seen very clearly. Thefirstpartofthefigureshowstheendofadischargeprocess.During discharge thewater issupplied tothebottom ofthetank. The picture showsthatthe course of the temperature of the water that is sucked from the tank after the charging process has started (the curve labelled 6, starting at t=5 hours) is mirrored compared to the course of the temperature of the water pushed into the tank in the hoursprior tot=5 hours(the curve labelled 4).However, apart of curve4cannot 55  Thegreenhouseheating system be found in curve 6. This isbecause thepipe that sucks thewater from the tank during charge ispositioned higher inthetank than thepipethat pushes thewater intothetank duringdischarge. Thewaterbelowthispiperemains relatively cold, whichleadstothepeculiarity discussed inthecomments inFig. 4.19.Theposition of thispipe is alsothe reason for the relatively small time span between the rise of the temperature at Sensor 3 and the rise of the outlet temperature during the charging process (Sensor 6).  Temperature [°C] 70 ^_  supply during charge  -r — »  -.  —  - «•*  •"*^rl*^^*1  _^*^  60-  h  50-  outlet during / discharge  40-  i  ^~ ^ N J f.'  t  •Z^®  '.y^ f V-outlet during /• /.' '•]/charge  ?nsupply during discharge • —»  0  i  i  i  i  .  2  .  (  4  .  .  -  >—• !  6  '  '  '  I —'•—'  8  • ' ' I  10  <  '  '  12 time [hours]  Figure 4.20 Comparison of model-outputwith measurementfor the chargeof a heatstoragetank. The numbersrefertofigure 4.18(• •••=measured, = simulated, = temperature ofsupply water).  4.4.6.3Conclusions The model proposed todescribe thestorage and extraction ofheat from astorage tank compares satisfactorily with measurements on a storage tank at one of the research facilities inIMAG-DLO. Byapplyingtheplug-flow modelonlyonemodellingparameter, namelythefraction ofthevolumeofacompartment thatresists in a cell of the shift register, has to be estimated. All other parameters of the model are simply geometrical data.  56  Modelsfor heatingsystem devices 4.4J Expansion system The expansion system takesaccount ofthevaryingvolume oftheheating system causedbythevaryingtemperatures. Thetankisattachedsomewheretotheheating system.Thepressure inthetank iscontrolled byacompressor, whichswitcheson whenthepressure dropsbeneath aparticular threshold (some 1.2 bar) andavalve that flushes airwhenthepressure exceedsanupperthreshold (some 1.6 bar).Fig. 4.21 shows a sketch of an expansion system.  supply andreturn pipe connectedto theheatingsystem  Figure4.21Expansion vessel. Whenthemean temperature oftheheating system increases,water flows intothe expansionvessel.Inthisstudyitisassumedthatthisfresh watermixescompletely with the water already in the vessel, which is likely since the fresh hot water enters the vessel at the bottom. Thus, the temperature of the water in the vessel after a certain amount of fresh water has entered can be computed by aweighed meanoftemperatures.Theweighingfactors arethewatervolumeintheexpansion tankbefore theentranceofthefresh waterandthevolumethat entered theexpansionvesselThe inflow ofwater iscomputed from thecubicexpansion coefficient of water (0.21-10'3 K"1)and the temperature change in the different components in the heating system, each rated according to their volume. When the water in the expansion vessel has atemperature that ishigher than the temperature of its surrounding, the vessel looses energy through its uninsulated wall. Insulation of the vessel in order to decrease its heat loss is discouraged by 57  The greenhouseheatingsystem installers because it appears that current expansion vessels do notwithstand continuously high temperatures. Tocompute the energy loss,thetank isdivided intotwosections.The lower part of the tank is assumed to havethe temperature of the water insidethe tank. The temperature oftheupperpartiscomputed from aweighedmeanofthewatertemperature andthetemperature ofthesurroundings. Thetemperature ofthewateris weighed according to the surface of the interface between the lower and upper partofthevessel(thecrosssectionofthevessel) andthesurrounding temperature is weighed according to the surface of the upper side of the vessel. The height of the lower side is computed from the current water volume in the tank and the area of the cross section of the tank. Theconvective heatexchangecoefficient ofthevessel iscomputed from aNu-Gr relation readingNu=0.11Gr°33.Thisyielded aconvectiveheatexchange coefficientof 1.44 AT033Wm"2K"'. Tothisconvectiveheatexchangecoefficient aradiativeheatexchangecoefficient wasadded,assuminganemission coefficient of0.8.  4.5 ASSEMBLING THE HEATING DEVICE MODELS  In theheatingsystem allheating devices,apart from thecondenser, are connected to each other by means of the main supply pipe (see Figure 4.3). The condenser isconnectedtotheupperheatingcircuit.However, duringperiods ofhighheatdemand, hotwater from themain supplypipecanbeaddedtotheupper heatingcircuit. Obviously, on these occasions the efficiency of the condenser will bedecimated. This practice,therefore, is a compromise between ahigh condenser efficiency throughout the year and an extra heating circuit. In contrast to the situation in aworking greenhouse, which as arule is divided into anumber of growth-compartments, each having their own heating circuits, the simulation model considered inthisstudy limits itself to a description of one set of greenhouse air conditions only. Thus, the heating system comprises only twoheatingcircuits.However,thetheorypresented belowdoesnotexcludeanextension in the number of heating circuits fed by the heat producing devices.  4.5.1 Model assumptions The contribution ofeach oftheheating devicestotheproduction or consumption ofheat inareal greenhouse heating system is commonly controlled bythe position of mixing valves. The valves are actuators in single loop controllers that attempttorealize atemperature setpointofthewater directlybehindthevalve.By passing a suitable set of setpoints, the heating system controller manages the 58  Assemblingtheheatingdevice models opening, closing and mixing ratio of the appropriate valves. Thecustomary timespannecessary tobringamixingvalve from theoneextreme position totheother isabouttwominutes.However, duringnormal operation the requested mixing ratios donotchangevery quickly (see thediscussion on Figure 4.24).Therefore, asimplification ofthemixingvalve dynamics byassumingthat required mixing ratios are instantaneously realized is allowed. The greenhouse climate controller generates setpoints for theheating circuits and control signals to the boiler, in order to produce C0 2 , and to start or stop the combined heat and power engine. In a well-engineered heating system in a greenhouse, the valve positions of the heating circuits (Vupp and Vlow) do not affect flows through these circuits.Thus, theseflowsareassumed tobeconstant.Theother flows intheheating system are assumed tobe controllable bymeans of a frequency controlled pump or abypass configuration. These variable flows can be controlled by single loop controllers that maintain appropriate pressure differences in the heating system.  4.5.2 Computations Figure 4.22 serves as a guide throughout this section. This figure is a copy of Figure 4.3,but hasbeen extendedwith references toparticular valves, flows and temperatures.  Figure 4.22Flowsandtemperatures intheheating system. Aheating system with astorage tank, asisthecase inthe greenhouse considered in this study, has two operating modes: charging and discharging. The situation inwhichastoragetankneitherfillsnorempties iscovered bythechargingmode, 59  Thegreenhouse heating system but with a charging flow zero. Thecomputations startwiththeformulation ofgeneralequationsfor therequested flow totheupper and lowerheatingcircuitandthetemperature ofthewater inthe gatheringpipe,allasafunction ofthetemperature ofthemain supplypipe.Then, thecomputation ofthechargingflowtothestorage tankwill bepresented for the situation where the heat produced exceeds the heat being demanded. Thereafter the discharge flow and, if necessary, the additional heating power will be computed.  4.5.2.1Flowsto the heating circuitsand thegatheringpipe temperature The supply side temperature in the upper heating circuit, TSupUpp iscontrolled by themixingvalveV .Inorder tosatisfy thesetpoint for theupperheating circuit (Setpupp) the mass flow resulting from the mixing ratio of Vupp is expressed by: <Psupp->upp - ™ * { 0. c p u p p S T P T u P P - ~ T T R e t U p P } vv vv yy k supply 'RetUpp  [ k g m - V ] (4.25)  with (puppthe mass flow through the upper heating circuit (determined by itscirculationpump), TRelUppthereturn temperature oftheheatingcircuit andTsupp|ythe temperature ofthemain supplypipe.Themaxoperator prohibits negativeresults. Withoutthisoperator thecomputed massflowwould benegativewhenthedistribution circuit cools down. Analogue toVupp, V|0Wcontrols the mixing ratio of hot supply water with return water from the lower heating circuit. <Psupf~low = max {0, < p t o w ^ P | o w~_*«V™ } 1  supply  l  [ k g m V ] (4.26)  RetLow  where the meaning of the variables is analogue to the Eqn. 4.25. The mass flows from thereturn sides of the distribution circuits tothe gathering pipe are equal to the mass flows <psupp_»upp and (psupp_»,ow. Thus, providing the absenceofashortcut betweenthemain supplyandgatheringpipethetemperature of the gathering-pipe is expressed by: j  _ ^supp-mpp *RetUpp ^supp-mpp  ^supp-frlow * RetLow  ropi i» yi  ^supp-Mow  If there is a shortcut between main supply and gathering pipe, Eqn. 4.27 would have to be extended with an extra term in both the nominator and denominator. The mass flow through the gathering pipe ((pgath) is the sum of ysupv^>upv and Tsupp->low  60  Assemblingtheheatingdevice models 4.5.2.2Chargingflow tothe storagetank The fact whether the storage tank is charging or discharging can be determined by comparing the sum of the required power of the distributing pipes with the currently produced reject heat from combined power and C02-addition. The current power demand PD of the greenhouse is determined by: P  D = c p (<PuPp(SetPupp-TRetUPp)+ 'Plow(SetPloW-TRetLow)) t W m" 2 ] (4-28)  with cpthe thermal capacity ofwater (Jkg^K"1). The current power supply from CHP (PCHP) and C02-addition (Pc02) is given by the status (on or off) and the thermal heating power associated with the on-status. In case (PCHP + PC02) > PD the heating system is in charging mode, otherwise the heating system is in discharging mode. When thestorage tank isbeingcharged, thetemperature of themain supply pipe (Tsupply) is equal to the charging temperature of the storage tank (Tcharge). In the present work Tchargeis set to90 °C.The mass flow tothestorage tank (cpsupp^st0) has such a level that the power surplus is absorbed. This flow can be computed easily by: P  CHP+ PCQ2 ~ PD rkem-Y'l (429) W * * , (T supply -T sto>bot ) cp ^ J <4-29> T sto,bot' s t n e temperature atthebottom ofthestoragetank.Incasethestoragetank isalmost completelyfilled,(p^p^ogrowstoinfinity. Whenthisoccurs,thesimulationmodel pushestheheatextentintothelower heatingcircuittobecarried off. =  4.5.2.3Dischargingthe storage tank TheheatingsystemswitchestodischargemodewhenPDexceedstheforced power supply. In order tobe ableto serve the heat demand of both heating circuits,the temperature of themain supply pipe must be at least ashigh asthe maximum of the setpoints. Thus: T  supp,min - *°* { Setp upp , Setplow }  p c ] (4.30)  with T min the minimal temperature for the main supply pipe. Consequently, when thestorage tank isbeingdischarged, Tsupp,yisavariable between Tchargeand T supP.min-T h e first t i m e a f t e r a P e r i o d o f char 8 in g> the o u t l e t o f t h e storage tank maintains the temperature at which itwas charged. However, duetoheat losses, andespeciallywhenthetankhasbeendepletedtoacertain extent,thetemperature attheoutletofthestoragetankwilldrop.ThenTsupplyisdetermined bythemixing ratio of the water coming from the storage tank, with a temperature Tst0 and water from the power sources, with a temperature Tcharge. 61  Thegreenhouse heating system Thetemperature ofthe supply water affects the flow required to feed theheating circuits (seethe denominator inthe equations (4.25) and (4.26)) and,with it,the temperature of the water in the gathering pipe. On its turn, the temperature at which the power sources are fed (having the temperature of the gathering pipe) determines theflow through thesedevices and,asaconsequence,thesupplytemperature. Obviously,thechainofrelationsendsat itsstartingpoint.Becausetheconnection of heating devices isbased on a static computation scheme the flow through the storage tank that balances heat demand and heat production is computed by an iteration. Thetemperature ofthegatheringpipedetermines themassflow through thecombined heat and power engine and the boiler. <PCHP= 7T  P  ^ charge  toiler = av  P  -HT  1  c  gath-' p  _°T  charge  [kgm"V1](4.31)  ^c u)c  (432)  frgW]  gatrK p  Obviously (pboUerhas to carry off theheat associated with carbon dioxide supply. The remainder of (pgath, after cpCHP and (pboi|er are withdrawn from the gathering pipe, flows into the storage tank. At the outlet, the same flow, having the temperature ofthetopofthestoragetankismixedwiththewater from thepower sources, yielding a supply water temperature according to: T SU  — PP'y"  power*charge  ^ g a t h ~ ^power* sto.top <Pgath  r°C (A 11 l  J (  with cppower= cpboi|er+ (pCHP. As long asTsupplyexceeds Tsuppmin,theheating power of the storage tank and the forced heating power are sufficient to cover the heat demand of the greenhouse. However, in case the storage tank isalmost depleted, thetemperature ofthewatercomingoutofthetankdropsandthesupplytemperature becomes too lowto feed theheatingcircuits. Thus,theboiler has toproduce additional power. IntheheatingsystemdepictedinFigure4.22,theadditionalpowerfrom theboiler is supplied to the heating system by diverting a fraction of the discharge flow through the boiler, by means of mixing valve Vadd. This flow is computed by: (P  -ffgath supp.min'^power*charge~v(Pgath"(Ppowep'*sto.tnn [ k g ^ e - h (4 34} charge  —  ^stOjtop  The final power to beproduced by the boiler is determined by: P  62  boiler = P C 0 2 + <Paddc p ( T su PP ,req ~ T sto,top)  [Wm" 2 ] (4.35)  3  Assemblingtheheatingdevice models Notethatthe additional power isaddedtothepower associated withC02-enrichment of the greenhouse air. Thestoragetankiscompletelyemptiedwhenthetemperature attheoutletislower than or equal to the temperature in the gathering pipe. In that case the heating system switchesbacktochargingmode,although in generaljust after adischargingperiod the charging flow will bezero.  4.5.3 Results To show the behaviour of the heating system the heating power of the boiler, a numberoftemperatures andvalvepositionsandtheperformance ofthecondenser ismonitored duringonedayinspring(2April).Thegreenhouseclimatecontroller settings and building and equipment characteristics are described in Section 6.3. Figure 4.23showsthecourseoftheheatingpower oftheboiler. Thecurveshows a peak around 06:00 hours and another one at 22:00 hours. The first peak originates from the greenhouse airtemperature setpoint increment from night todaylevel.The secondpeak marks themoment that theheat storage tank isempty.At that moment the boiler takes over the heat supply. The constant levelof thecurve between 11:30and 17:00hours iscaused by C0 2 supply with exhaust gases.At 18:00 hours the boiler is switched off.  Heatingpower [Wm1]  0  4  8  12  20 24 time [hours]  Figure4.23Heatingpower ofthe boiler. In Figure 4.24a, from the dotted decreasing line can be seen that between 18:00 and22:00hourstheheatdemand ofthegreenhouse iscoveredbytheheatstorage tank.Thestoragetankhasbeen filled intheprecedinghours.Duringthecharging period the mean storage tank temperature has increased from 36 °C to 60 °C. Thus, on this day, at the end of the charging period the tank was filled for only 44%.Duringthechargingperiod thetopofthetank increases toTchargequite fast, 63  The greenhouse heating system  whereas the bottom of the tank remains at 35 °C. From 11:00 till 15:30hours, as can be seen in Figure 4.24b, the mixing valves of both the upper and lower heating circuit are closed. As a consequence, the water in the gathering pipe is not refreshed by return water from the heating circuits, and because the heating system model doesn't take account for heat losses in transport pipes, the temperature of Tgalh remains constant at 30 °C (see Figure 4.24a). At 15:30 hours the mixing valve of the lower heating system opens to a mixing ratio of 0.15. From that moment, Tgath is governed by the return temperature of the lower heating circuit. First Tgath decreases to 28 °C, which is the temperature to which the lower heating circuit has cooled down in the preceding period, and then increases to about 40 °C. A similar course, but damped, can be found in the temperature at the bottom side of the storage tank because, during discharge, the water from the gathering pipe flows into the bottom side of the tank. Eventually the bottom side temperature becomes equal to T ath (20:30 till 22:00 hours). Temperature [°C] 10090  main supply pipe BBWWOPftOOOOOa  storage tank top 80 70- | storage tank mean 60-  gathering pipe..  40Of) —i  ou  ::  ''N.-; '  50-  y storage tank bottom•  /  N-  '*  -—^—»^—  12  16  20 24 time [hours]  Valve position [-] 0.5  lower heating circuit upper heating circuit additional flow control  12  16  20 24 time [hours]  Figure 4.24 Thecourse of temperatures (a)and valvepositions (b) during one day 64  Assemblingtheheatingdevice models Starting at 20:00 hours, after the tank has been discharged for two hours, the temperature atthetopofthetank startstodecrease.At 19:45thetemperature has become that low that the temperature setpoint for the lower heating circuit (not shown in thepictures) can no longer berealized. At that moment the valveVadd openssomewhat(seeFigure4.24b)toincreasethetemperature ofafraction ofthe water from theheatstoragetankto90°C(seesection4.5.2.3).However, at22:10 hours thetemperature ofthewater withdrawn from thetank becomes lower than Tgath.Onthat moment theheatingsystem switchestocharging mode(with charging flow 0), meaning that the supply pipe temperature becomes 90 °C and Vadd closes. In Figure 4.24b can be seen that, for a short time (05:00 till 09:00 hours) the temperature oftheupper heatingcircuit iscontrolledbyVupp.However,theupper heating circuit is used to carry off the heat gathered with the condenser aswell. Thus, itcanbeexpectedthat intheconsidered timespanthecondenser efficiency drops. Indeed, this appears to be the case, as can be seen in Figure 4.25. In this figure, thecondenser efficiency isdefined analoguetoFigure4.13.Fortheperiod that theboiler isswitched off (18:00 till 22:00 hours) thecondenser efficiency is not defined.  Condenser efficiency [-]  0  4  8  12  20 24 time [hours]  Figure4.25Condenser efficiency. Finally, in Figure 4.26 the return temperature of the upper heating circuit is shown.Apart from theperiod between 05:00 and 09:00 hours,the upper heating circuit (and the return temperature) is governed by the heat production of the condenser. Note that the upper heating circuit cools down between 18:00 and 22:00. In this period the condenser does not produce heat because the boiler is turned off.  65  The greenhouse heating system  Return temperature upper heating circuit [°C]  20 24 time [hours] Figure 4.26 Return temperature of the upper heating circuit.  66  Introduction 5. GREENHOUSE CLIMATE SIMULATION  5.1 INTRODUCTION  The simulation of greenhouse air temperature, humidity and carbon dioxide concentrationprovidesthefeed-back quantities for thegreenhouseclimate controller. In turn, these quantities are aresult of climate control actions inthepast. In this chapterthemodelling ofairtemperature, humidity andcarbon dioxide concentration,hereafter denoted asthegreenhouse climate,ispresented asafunction ofthe actions of the greenhouse climate controller and the environment of the greenhouse. As discussed in Chapter 3, the simulation of these three quantities is performed by numerical integration of their differential equations. In order to describe the differential equations,alargenumberofotherquantitieshavetobedefined. Some of these quantities are aresult of numerical integration as well. Tokeepthepresentationconvenientlyarranged,thegreenhouseclimatesimulation model issplit intothree sub-models: athermal model, awatervapour model and a C0 2 model. These sub-models are discussed separately in Section 5.3 (the carbon dioxide model), Section 5.4 (the water vapour model) and the large section 5.5,wherethethermalmodelispresented.However,before discussingthespecific sub-models, the notational conventions applied are presented in Section 5.2.  5.2 NOTATIONAL CONVENTIONS  The greenhouse climate simulation model which isthe subject of this chapter, is based onthedefinition ofendogenous statevariables, fluxes andboundaryconditions, as formulated in Section 3.2. Because there is a high level of similarity between the equations that play a role in the models, a consequent notation for state variables and fluxes is adopted. In the sections below the conventions are presented.  5.2.1 State variables In the greenhouse climate simulation model three types of statevariables canbe distinguished(seeFigure3.1).Themajority ofthestatevariablesrefer totemperatures.Thesevariables are denoted bynames beginningwithacapital T, followed by athree characters subscript, whichrefers tothestatevariable in consideration (e.g. Tair). The other state variables comprise the partial pressures of vapour, denotedbythecapitalsVP,andthepartialpressure ofcarbon dioxide.Statevaria67  Greenhouse climate simulation blesinthe C0 2 model aremarked C02.The subscripts areequaltotheonesspecifying the thermal state variables (e.g. VPair and C02air). Temperatures are expressed inKor °C,whatever isthe most convenient. Partial vapourandcarbon dioxidepressures areexpressed inNm"2(which isequaltoPa).  5.2.2 Fluxes Thesimulationmodeldistinguishesheatandmassfluxes.Unlessexplicitly defined as being different, all fluxes are expressed per m2 ground surface of the greenhouse.Mostfluxesare the result of adifference between the level ofstate variables,butsomefluxesareforced byboundary conditionsorclimatecontrolactions. Forced heatfluxesaremarked with acapital P, followed by asubscript. Thesubscriptismadeupoftwoparts,codingfor thesource anddestination compartment oftheflux(e.g. PAiucan>which refers toaheat flux from artificial illumination to thecanopy).Heatfluxesassociated with condensation orevaporation ofmoisture begin with a capital L. Forced fluxes of carbon dioxide are denoted by a capital C, followed by the familiar subscript (e.g. CConAir, which refers to the carbon dioxide input from the greenhouse climate controller to the greenhouse air). Forced vapour fluxes do not occur in the present model. Sensible heat fluxes are marked with a capital H, when they refer to convective orconductiveexchangeprocesses,andaremarked withacapitalRwhenradiative heatexchange isinvolved.Thecustomary subscriptsare suffixed (e.g.HAilCovand Massfluxesinthewatervapourmodel aremarked bythecapitalsMV(for exampleMVCanAir).ThefluxesintheC0 2 model areindicatedwithMC(e.g.MCAir0ul).  5.2.3 Exchange coefficients Allfluxesinthemodelthatarecomputedfromadifference instatevariableshave anexchange coefficient that governstheexchangeprocess.Exchange coefficients for computing a convective orconductive heat flux are termed HEC,suffixed by thesame subscript asthefluxgoverned bytheexchangeprocess under consideration. For instance, the exchange coefficient for the heat exchange between the upperheatingpipeandthegreenhouseairistermed HECUppAlr.Withthisexchange coefficient the equation for computing the convective heat release of the upper heating pipe to the air can easily be stated as: "uppAir = HEC UppAir (T upp - Tair)  [Wm"2](5.1)  Radiative exchangeprocesses are governed by the Stefan Boltzman equation. To stressthatitisanon-linearrelation,exchangecoefficients involvingradiativeheat 68  Notational conventions exchange are termed REC. Again the suffixed subscript refers to the exchange process under consideration. Thus an equation expressing a radiative heat flux looks like: RLowCan = R E C L o w C a n (T, o w 4 - T c a n 4 )  [Win 2 ] (5.2)  However,allradiativeexchangeprocessesassociated withthethermal screenlinearized. To express this linearization, the exchange coefficients involving these radiativefluxesarecategorized asHEC.Thus,for example,theheatexchangebetween upper heating pipe and the thermal screen is described by: R  UPPScr = HEC UppScr (T upp - Tscr)  [Win2] (5.3)  Theexchange coefficients for massexchangeprocesses beginwithVEC inequations on vapour exchange and with CEC where C0 2 exchange rates are being computed. Examples are: and  MV  AiK:ov = VEC AjrCov (VPair - VPC0V)  [kgs-W2] (5.4)  MC  AirTop = CEC AirTop (C02 air - C02 top )  [kg^W 2 ] (5.5)  Evaporation and condensation of vapour are treated asmass exchange processes.  5.2.4 Exogenous variables The greenhouse climate simulation model includes six exogenous state variables (or boundary conditions) that, in flux computations, act inasimilar wayasendogenous statevariables. These sixvariables areTsky,Tout,VPout, C02out, Tlow,Tupp andTMl (see Figure 3.1). The fact that the temperatures of the upper and lower heating pipe are categorized as exogenous variables may surprise, since thepipe temperature was an endogenous state variable in Section 4.4.1. However, aswas discussed in Section 4.4.1.4, theresult of theheating circuit simulation ispassed tothe climate simulation model asthe mean temperature of the pip segmentsrepresenting the distribution loops. Thus, the pipe temperatures of the upper and lower heating circuit act asboundary conditions with respect to the thermal submodel of the greenhouse climate simulation. Exogenous flux variables are the intensity of direct and diffuse solar radiation. Although these radiation intensities are forced fluxes they are referred to asIdir and Idif (and not with designations beginning with P), because they act in avery different type of equations.  69  Greenhouse climate simulation 5.2.5 Other variables Structured naming only makes sense ifequations orprocedures haveahigh level of similarity. Since a high level of similarity lacks the relations which do not confine oneofthetypesmentioned above,thenamingofothervariables thatplay a role inthis study cannot be discussed in a general section.  5.3 THE CARBON DIOXIDE SUB-MODEL  Thecarbondioxidesub-model includestheC0 2 concentration ofthetopcompartment (C02top) and the greenhouse air compartment (C02air). However, when the thermal screen isopened, or not available,the air compartment andthetop compartment are lumped together. The structure of the sub-model is presented first and subsequently the computation of the fluxes is discussed.  5.3.1 Structure of the carbon dioxide model Agraphicrepresentation ofthestatevariables andthe fluxes distinguished inthis sub-model ispresented in Figure 5.1.The endogenous and exogenous statevariables are represented analogue to Figure 3.1.  Figure5.1Statevariables,fluxesand theexogenousvariableintheC02 model. The two state variables of the C0 2 model are connected by MCAirTop, describing the C0 2 transfer between the top compartment and the greenhouse air compartment when the screen is(partly) closed. The top compartment looses C0 2 tothe outside air, described by MCTop0m. The outside partial C0 2 pressure (C02out) is assumed tobe constantly 34Pa (»340 ppm). When the screen isopened, adirect 70  Thecarbondioxide sub-model air exchange between the greenhouse air compartment and the outside air can occur. Thisexchange isdescribedbyMCAir0ut.Besides aC0 2 losstothetopcompartment or the outside air, the greenhouse air compartment looses C0 2 to the canopy (CAirCrp). The climate controller supplies C0 2 to the greenhouse air by means of CConAir.These last two mass flows are considered forced fluxes. With the fluxes shown in the figure and the theory presented in Section 3.3 the differential equations for the state variables can be stated easily: dC02 top dt  MC  dC02 air dt  C  AirToo ~  MC  TopOut  ^cV t o p /(RT)  [Pas"1](5.6)  and ConAir~ M C AirTop~~C AirCrp"~M C AirOut  M c V air /(RT)  [Pas"'] (5.7)  The dependency of the capacity on the air temperature is neglected by using a constanttemperature of291K.Vair,thevolume ofthe C0 2 compartment iscomputedwiththemeanheightofthegreenhouse.The application ofaconstantvalue for Vairneglects the decrement ofthe air volume represented by C02airwhenthe screen is closed. However, since the top of the greenhouse contains only about 10%oftheairvolume,andtheheatcapacity ofair issmall already,thedynamics of the C0 2 concentration are of minor importance. Therefore this neglection is obliged. Mc is the molar mass of C 0 2 , (44 kgkmor1) and R the gas constant (8314 Jkmol-'K-1). By(numerical) integration ofEqn. 5.7 thecourseoftheC02-concentration inthe greenhouse air can be determined intime. As said,thecapacity ofthetopcompartment for C0 2 isonly 10%ofthe capacity ofthemain air compartment. Consequently, the dynamics ofthiscompartment is ofa small timebasecompared tothemean dynamics oftheother compartments. Therefore the C0 2 concentration in thetop compartment isnot computed by numeric integration but by a static equation, implying dC02top/dt to be zero. After rewriting MCAirTopwithequation 5.5andMCTop0utwithananalogueone,and after solving C02 top from this equation the expression yields: C02 t o p =  CEC Ton0u , C02 out + CEC AirToD C02 air I2EQSL; +CFC "  tPal  ^  71  Greenhouse climate simulation 5.3.2 Fluxes in the carbon dioxide model IntheC0 2 modelthreeC0 2 exchangeprocesses andtwoforcedfluxesareconsidered to play a role. The exchange processes are related to the ventilation flux throughthewindowsandtotheairexchangeratethrough openings inthethermal screen. The forced fluxes are the C0 2 consumption of the canopy and the C0 2 supply by the greenhouse climate controller.  5.3.2.1 Exchange processes The ventilationfluxthrough thewindows isdenoted byf^,,, andtheair exchange ratethroughthethermal screen isdenotedbyfAirTop. Boththese airexchangerates are expressed in m3m"2s'', where the surface refers to a m2 floor area.fventand fAirTop are defined in Section 5.5.2. TheC0 2 flux betweenthegreenhouseandtheoutsideairispresented asanexample. Using the gas law for ideal gases and application offventto describe the air fluxbetween greenhouse and outside air outward C02 flux is defined by:  Mc A i l 0 u t = ¥&** ( 2 2 2 * - ^ o u t )  [kg5,m.2]  (5 9)  withMcthemolar massofC0 2 (44 kgkmol"1).Theexpression for MCAir0ul isnot linear.Linearization oftheexpression byapplication ofameantemperature introduces an inaccuracy that goes up to some 15%for large temperature differences. Therefore, the definition of an exchange coefficient such as applied in Equation 5.5isomitted.Whenthethermal screen isnotopened,themodel concept excludes MCAir0ut by assigning zero to the flux. Contrary tothenumeric computation of C02air,wherefluxesgovern theequation (see Eqn. 5.7), the algebraic computation of C02top (Eqn. 5.8) requires linear equations for the fluxes (like Eqn. 5.5), rather than fluxes. Thus the non-linear relations for MCAirTop and MCTop0u„ which can be stated analogue to Eqn. 5.9, havetobe linearized inaC0 2 pressure difference. Thislinearization is performed by neglecting the density differences between the air temperatures, by using a mean temperature of 287 Kinthe equation for CECAirTop and 283 Kintheequation for CECTop0ut. The error made by this neglection goes up to 10%, but accepted because the C02-losses are small anyway during periods with a closed thermal screen. Thus the exchange coefficients are described by:  72  M, CEC AirTop = 28fR fAirTop  [kgs-m-Pa-'] (5.10)  Mc lvent CEC ^ J SR TW T o n 0 u t = T283 "TopOut  [kgs-'m^Pa-1] (5.11)  Thecarbondioxide sub-model 5.3.2.2 Forced fluxes The C0 2 supply to the greenhouse air compartment by the greenhouse climate controller (CAirCon) is an on/off flux. When on, the rate is determined by the amount of exhaust gases combusted in the boiler. Denoting the combustion rate of natural gas in m3 per second per m2 floor surface as <(>*,and with the C02 content of exhaust gases of 1.76 kgper m3 combusted gas (see Section 4.4.4.1) CA>rConis  defmed  b  y;  CConAir= <t»*l-76  [kgs'W 2 ] (5.12)  The second forced flux in the C0 2 model is the carbon dioxide fixation by the canopy (CAirCan). This C0 2 assimilation process isdriven by shortwave radiation. However, the relation between radiation and assimilation rate is quite complex. Therefore the discussion on this matter is presented in Appendix I.  5.4 THE WATER VAPOUR SUB-MODEL  Thesecondsub-model concernsthehumidity inthegreenhouse.Thewatervapour model includesthepartial vapourpressure ofthetopcompartment (VPtop)andthe greenhouse air compartment (VPair). Analogue tothe C0 2 model,theair- andtop compartment arelumped togetherwhenthethermal screen isopened,ornotavailable.Inthissection,thestructure ofthesub-model ispresented first, followed by a computation of the fluxes.  5.4.1 Structure of the water vapour model A graphic representation of thestate variables and thefluxesin thewater vapour model arepresented inFigure 5.2. Thepartial vapour pressure ofthe greenhouse aircompartment isincreasedbyevaporation from thecanopyanddecreased byair exchange and condensation at the cover and screen. Evaporation and condensation depend onthevapour pressure difference between air and the vapour pressure at a surface. The latter is defined by the saturated vapourpressure for itstemperature (seeAppendixH).Therefore, thevapourpressureatasurface isaresult from thethermal sub-model. Thus,inthewatervapour modelthevapourpressure atthecanopy,thescreen andthecoveractasboundary conditions.Consequently, inFigure 5.2 VPcan,VP^ and VPC0Vareplaced inopen boxes. When the vapour pressure at the cover is lower than VPair condensation takes place at the inner side of the cover. In modern greenhouses the condensate is drained. Therefore evaporation of moisture from the cover to the air (when the  73  Greenhouse climate simulation covertemperature increases) canbeneglected. Whenthethermal screen isclosed, direct condensation of moisture from the greenhouse air below the screen to the cover (MVAjrCov), andthe direct lossofmoisture byventilation (MVAir0ut) isprohibited.  MV,  Figure 5.2State variables,fluxesand boundaryconditionsinthe water vapour model. Becausethescreen cannotproducevapour, evaporation from theuppersideofthe thermal screen, accounted for by MVScrTop, is possible only when condensation takesplaceatthelower sideofthescreen, denoted byMVAirScr. Obviously, when the screen is not porous, MVScrTop is always nil. The capacity for moisture of the top compartment is very small. Therefore, the vapour pressure of the top compartment is computed by an algebraic equation, analogue to Eqn. 5.8. VP,oP = (VEC Top0ut VP out + VEC AjrTop VP air VEC  [Pa] (5.13)  TopCovVPcov+ VEC ScrTop VP top ) /  (VEC Top0ut +VEC AirTop+ VEC TopCov +VEC ScrTop ) The vapour pressure of the greenhouse air is computed by numerical integration ofthedifferential equation ofthemoisture content ofthegreenhouse aircompartment. The differential equation for the moisture content of the greenhouse air compartment reads:  74  Thewatervapour sub-model dVP • =  1  (MVc  ST M^iTf)  ^<- MV *«°P-  [Pas (514)  '  ^AirScr - MV AllCov - MV Ail0nl ) The term that expresses the capacity for moisture is almost the same astheterm for thecapacity of the greenhouse air for C0 2 , except for the molar mass,which holds for vapour (18 kgkmol"1). Eqn. 5.14 shows that the capacity is a function oftemperature. However,just likethe case inthe C0 2 model,thepresent model appliesaconstantcapacity,holding for atemperature of291Kandameangreenhouse air volume above one m2 floor surface. IntegrationofEqn.5.14yieldsthecourseofthevapourpressureofthegreenhouse air in time.  5.4.2 Fluxes in the water vapour model Inthe water vapour model all fluxes result from convective exchange processes. The computation of the mass flux from the greenhouse to the outside air by ventilation (MVAir0ul) is analogue to Eqn. 5.9. Mf VP - VP MV A i t 0 u t = - * j f * ( - ^ --SX) ^ 'air 'out  [kgs-'m-2] (5.15)  withMHthemolar mass ofvapour and £,„,theventilation flux (mV'm' 2 ). When the thermal screen is not opened MVAir0l)1is made zero. As in the case of the C0 2 model, to compute the humidity of the top compartment, only the exchange coefficients are of interest. The exchange coefficients related to air exchange are defined analogue to Eqns. 5.10 and 5.11. VECAirTop= M  f  AirTop  f vent VEC-ronOut -TopOut= W283VR lvent  [kg^'m^Pa"1] (5.16) [ k g s V P a 1 ] (5.17)  The masstransfer from theairtothe screen andthecover (condensation) isgovernedbyprocessesattheboundarylayeratthesesurfaces. Becauseofthesimilarity of thetransport mechanism for vapour and heat transfer through the boundary layer,themassandheattransfer coefficients arecorrelated.Thetheoryconcerning this relation is presented in Appendix B. There a factor 6.4-10'9 kglCT'Pa"1 is found between the heat and mass transfer coefficients. Because theheat exchange coefficients arewell described (see Appendix A),the mass transfer coefficients for condensation and evaporation at thescreen andthe cover can becalculated. Thus VECAirScr,VECScrTop, VECAirCov and VECTopCov are computed bymultiplyingthecorresponding heatexchangecoefficient by6.4-10*9. 75  Greenhouse climate simulation For example: VECAirCov= 6 - 4 - 10 " 9 ^ A ^ o v  [ k g ^ P a 1 ] (5.18)  The mass fluxes are computed from the mass transfer coefficients and vapour pressuredifferences withequationsanaloguetoEqn.5.4.However, contrarytothe mass fluxes resulting from air exchange,theevaporativefluxesand fluxes dueto condensation are prohibited from being negative. This is because the model excludes evaporation from the cover and lower side ofthescreen. Condensation on the upper side of the screen is prohibited as well. The negative fluxes are prevented by making the mass transfer coefficients zero when the vapour pressure difference is negative. By allowing a mass flux MVScrTop, the present model assumes that the thermal screen is capable of transporting water from the lower side to the upper side through the fabric. This fabric will be ableto store some water. However, in the present modelthestorage ofmoisture inthe screenisneglected.This impliesthat vapour thatcondenses atthe screen iseither evaporated attheupper sideor drips from the screen. Another implication of the neglection of storage isthat the rate of evaporation at the upper side of the screen is lower or equal to the rate of condensation at the lower side. To avoid the screen evaporating more than the amount of water that condenses at the lower side of the screen, VECScrTop is restricted by: VEC ScrTop < VEC AirScr v  vp  VP a , r • - VP _ ypscr  vr  scr  vr  [kgs-'m-2Pa-'] (5.19)  top  The vapour flux from the canopy to the greenhouse air originates from aphase interface somewhere insidethecavitiesofaleaf.Thus,theresistance tothetransportofthisvapourfrom theleaftothegreenhouse airconsistsofaninternalresistance, formed bythe leaftissue andthe stomata, and aboundary layer resistance (Stanghellini, 1987).Theresultingmasstransfer coefficient isthereciprocal ofthe sumofbothresistances.Theboundarylayerresistanceiscomputed from theresistancetoheattransport.AccordingtoAppendixBtherelationbetweentheresistance to heat mass and heat transport reads r b v = Le M r b H  [sin1] (5.20)  with Le the Lewis number (0.89 for vapour). The computation of the boundary layer resistance to heat transport ispresented in Section 5.5.2 (page 87). Contrary totheboundary layerresistance,which isdetermined by micro-climatic conditions,theinternalresistance isactivelyregulated bythecanopy.Thisregulationtakesplace byalteringthe aperture ofthe stomata. As can beseen inmodels describing the stomatal resistance (Bot, 1983; Stanghellini, 1987;Jolliet, 1991), themajor factor inthiscontrol mechanism istheintensity of shortwave radiation. 76  Thewatervapour sub-model Other factors, but less pronounced, are the C0 2 concentration of the greenhouse air, the temperature of the leaves and the vapour pressure deficit between the leaves andtheambient (Stanghellini, 1987).For tomatoes, Stanghellini described theinternalresistanceasafunction ofshortwaveradiation,temperature, C0 2 concentration and vapour pressure deficit with a multiplicative equation. r  i,V = rmin tfs> r(T0> r ( C ° 2 ) r ( e 0" e a)  t s m "'] ( 5 - 21 >  rmin isthe minimum possible canopy resistance. The symbols r(Is), r(T0), r(C02) and r(e0-ea) represent functions larger than unity, describing multiplicative resistance components oncanopytranspiration duetounfavourable leaftemperatures, highirradiation levels,abundantC0 2 levelsandlargevapourpressure differences. The functions for the multiplication factors that were used in the model fitting procedure were: L + C,  H <5"22>  r(Is) = -f-Tcl  s  ^2  r(T0) = 1+ C3(T0 - T m ) 2  [-] (5.23)  r(C02) = 1+ C 4 (C0 2 - 200)2  [-] (5.24)  r(e0-ea) = 1+ C 5 (e0 - e a ) 2 [-] (5.25) Inthese formulas Isisthemean shortwave radiation flux, absorbed bythecanopy (Wm'2leaf), T0representsthecanopytemperature andTmthetemperature atwhich the resistance is minimal (°C). C0 2 refers to the C0 2 concentration (ppm) and (e 0 -e a ) represents the vapour pressure deficit (Pa). Stanghellini determined all variables for the daytime and the nighttime period (Table 5.1). Table 5.1. Values andunitsofparametersinthemodelofStanghellinifor tomato androse.Thevaluesfor tomato weregivenbyStanghellini. The values for rosewerevalidatedon behalfof thepresent work. tomato daytime  Ky «T 0 ) r(C0 2 ) r(e0-ea)  nighttime 658.5  c,  82.0 4.30  C?  0.54  c, Tm  c4 c5  illuminated roses daytime nighttime 140 10  180  sm"'  -  Win 2  1.25  -  WnV2  2.3-10"2  0.5-102  1.3-10"2  0.35 10-2  K-2  24.5  33.6  24.5  33.6  °C  0  0 5.2-10-*  PPm"2  6.1-I0  -  7  1.H0-"  6  6  4.3-10"  5.2-10"  3.6-10-*  Pa 2  In this study, on behalf of thevalidation of the simulation model an illuminated rose canopywasused.During thevalidation ofthemodel itappeared thatresults 77  Greenhouse climate simulation improved when the evaporation of arose canopy was diminished compared to a tomato stand. To achieve the diminished evaporation the stomatal resistance was increasedbyadaption ofthevariablesrmin,C,,C2,C3andC5.Theresultspublishedby Stanghellini andtheresults ofthemodel tuningwithrespect to illuminated roses are stated in Table 5.1. Because in the present work thevapour pressure (deficit) is expressed in Pa, instead of kPa, the constant C5 in Table 5.1 was multiplied by a factor 10"6compared the value reported by Stanghellini. Fortwoofthefunctions Stanghellini added arestriction onthevalue ofthe function. She limited r(C02) to 1.5 and r(e0-ea)to 5.8.Now themasstransfer coefficient can be determined by: ^C-Air =^  2 o c LAI ^ + r .y )  y(  ^ ^ ]  (5-26)  with p thedensity ofair (1.23kgm"3), cpthespecific heat ofair (1.0J kg"1),LAI the leaf area index, AH the latent heat of evaporation of water (2.45 106Jkg"1) and7thepsychometric constant (65.8 Pa K"1).The factor 2accounts for the fact that a canopy leaf has two sides,whereas the LAI refers to one side only.  5.5 THE THERMAL SUB-MODEL  Thethird sub-model isthemost extensivepart ofthegreenhouse climate simulation model. It describes the thermal statevariables.  5.5.1 Structure of the thermal model Thethermal model isshown inFigure 5.3.In thepicture the samedrawing conventionsareapplied asinFigure 5.1and 5.2,butinordertokeepaneatlyarranged presentation the boxes for TCov, TScr and Tp,,.are extended. Themajority ofthefluxes distinguished inthethermal model originate from heat exchangeprocessesbetweentheendogenousandexogenousstatevariables.However, a number of the forced fluxes demand some explanation. Thegreenhousecovertransmits mostofthesolarradiation,reflects afraction back totheatmosphere andabsorbs asmall fraction intheglass and itssupportingelements. The heat flux associated with this absorption is contributed tobyPSunCovFrom thetransmitted fraction, part isabsorbed by opaque elements inthe greenhouse (feet, girders etc.). Since these elements are not distinguished as separate entities, but directly release their heat to the greenhouse air, the energy flux associated with the absorption of these obstructing elements is assigned to the greenhouse air by a variable PSunAir 78  Thethermal sub-model  Figure 5.3Statevariables,fluxesand boundaryvariablesinthethermal model. Thecanopyabsorbsshort-waveradiation from thesunand,ifpresent, from artificial illumination. These short-wave heat fluxes are denoted PSu„canar*d^AiuCanre " spectively.Theshort-wave fluxestothecanopycontributetodirectabsorption,but 79  Greenhouse climate simulation alsofor absorbtion from secondary reflections from thefloor surface. Short-wave radiation that is not intercepted by the canopy is partly absorbed by the floor referred to by PSunFir and PA|uFlr, and partly scattered back to the sky above the canopy. Some of this radiation is intercepted by obstructing elements inside the greenhouse (some 10%), but the major part will leave the greenhouse envelope. Therefore the heat flux from short-wave radiation that isreflected bythe canopy and floor back to the greenhouse ambient is neglected. Besides generating short-wave radiation, artificial illumination supplies a significant amount of sensible heat. This heat flux is referred to by PA|uAir. The temperature ofthe heating pipes isdetermined by the heating system model (see Section4.4.1),andtherefore considered asaboundaryvariable inthethermal model. The other boundary variables, except for Tso7 are derived from hourly weather data. The temperature at 1.27 m below the floor of the greenhouse is computed by aperiodic function reading T so7 = 15.0 + 2.5 sin(1.72-10-2(<fajTir-140))  [°C] (5.27)  With daynrthenumber ofthe sequential day of theyear, with 1 January asdaynumber 1. From Figure 5.3,the heat balances can be stated easily from the addition of all energy fluxes toacompartment inanetenergy flux. For thecover thisresults in: ^  = p u l  c '  H  V  r COV v p , C O V  cov,net  P ^ ' ] (5.28)  COV  with H  cov,net= PSunCov+ HTopCov+ HAi,Cov+ RFl,Cov+ R  ScrCov+ RUppCov+ RLowCov+ ^anCov  ( Wm " 2 J < 5 - 29 ) +  ^TopCov+ LAirCov ~~HCovOut "~ ^ovSky  The density of the greenhouse cover (pCov) is 2.6-103 kgm'3 (glass) and the specific thermal capacity(cpcov) is840Jkg"3K''.Thevolumeofthegreenhouse cover compartment (V^) depends on the thickness of the glass (d) and the roof slope (|/) according toV^^d/cos^). Commonly dis4-10*3mand \i is25°.As inthe other sub-models, integration ofthe differential equation yields the course of the statevariable intime.Thefluxes mentioned inEqn. 5.29 arediscussed inthenext sections. Aswiththecarbon dioxide andvapour sub-model, thestatevariable representing thetemperature ofthetopcompartment iscomputed byastaticequation,because its heat capacity is very small. The net flux to the top compartment is stated in Equation 5.30. H  top,net  =  H  ScrTop+ HAirTop_ HTopCov" HTopOut  [Wm"2] (5.30)  The top compartment temperature that results from the requirement that the net 80  Thethermal sub-model flux equals zero is found by implementing the flux relations (analogue toEqn. 5.1) andyields: T  top = ( HEC ScrTop T scr + HEC AirTop T air + HEC TopCov T cov + HEC  t K l (5-31)  TopOut T out) / ( HEC ScrTop + HEC AirTop + HEC TopCov + HEC  TopOut)  The netfluxtothethermal screen isstated inEquation 5.32 Hscr,net = RFlrScr+ LAirScr+ RUppScr+ RLowScr+ H  t W m ' 2 ] (5-32)  AirScr+ ^anScr ~~HScrTop ~ LScrTop ~~RSrcCov  Because thecapacity ofthe state variable representing thescreen temperature is very small, like thetopcompartment, thescreen temperature iscomputed by an algebraic equation. This implies that Eqn. 5.32equals zero. Some heat fluxes stated inEqn. 5.32(RandL)arenotlinear inTscr.Toperform easy calculation they are linearized. The linearization of the radiative heat exchange is discussed in Section 5.5.2. The linearization of the fluxes associated with condensation andevaporation (LAirScr andLScrTop respectively) is performed by linearizing thesaturated vapour pressure curve. This linearization states that LAirScr = 2  A 5  ^ V E C AirScr (VP air - (,T scr +/))  [Wrn2] (5.33)  wheres istheslope ofthetangent atthesaturated vapour pressure curve around Tscr and/ itsintercept. Theslope ofthetangent iscomputed from thederivative ofthesaturated vapourpressure curve(seeAppendixH)andthe intercept follows from i=VPscr-sTsa.Intheexpressions forsandithelastcomputed valueforTscr and VPscr areapplied. Theexpression for LScrTop isanalogue toEqn.5.33. After substitution ofLAirScrandLScrTopbyequationssuch asEqn. 5.33,theconvectiveheatexchangetermsbyequations suchasEqn. 5.1andtheradiative heatexchangeterms byequations likeEqn. 5.3,andafter rearranging terms,theexpression for Tscryields: T scr =(A//(VECAirScr(VPair-/ )+VEC ScrTop (VP top -/))+ HEC  [°C](5.34)  AirScr T air + HEC UppScr T upp + HEC CanScr T can +  H E C L ^ ^ T ^  +HEC FlrScr T flr +HEC S c r T o p T t o p + H E C ^ ^ T ^ y  (A//(VEC A i r S c r +VEC S c r T o p ) s +HEC A i r S c r +H E C U p p S c r + " E C C a n S c r + H E C LowScr + HEC F l r S c r + HEC S c r T o p + HEC S c [ C o v )  with AHthe heat of evaporation. Theprevention of a greater evaporation than condensation wasalready accounted for inthecomputation ofVECScrTop. WhenobservingEquation 5.31and5.34,itappearsthattheequationsaremutually 81  Greenhouse climate simulation dependent becausethefirstusesTscrandthesecond usesTtop.Equations 5.31and 5.34 can be considered as a set of two linear equations in Ttop and Tscr, which shouldbesolved simultaneously. However, becausethecontribution ofTtopinthe computation ofTscrisvery small, inthepresent model thetemperatures arecomputed sequentially, starting with T^. Thenext statevariable inthethermal model represents thegreenhouse airtemperature.Just likethecasewiththeother sub-models,whenthescreen isopenedthe compartment alsorepresents the air inthetop of the greenhouse.The expression for the net flux to the greenhouse air can be read from Figure 5.3. H  =  air,net  P  AluAir + P SunAir + H UppAir + H LowAir + H  CrpAir -  H  [ W i n 2 ] (5.35)  AirFlr ~~ H AirTop ~ H AirScr ~ H AirOut ~ H AirCov  The rate of temperature change, resulting from this net flux is expressed in the same way as in Eqn. 5.28. ^ - p . c ' . V . Ul ^ a i r ^ a i r v air  H  [Ks' 1 ] (5.36)  air,net  The capacity of the air compartment, the denominator in Eqn. 5.36 varies with temperature because the density pair is temperature dependent. Nevertheless a constant density is applied (1.20 kgm"3), holding for 20 °C and standard atmosphericpressure (1-105Pa).Thespecific thermal capacity (cpair)issettoaconstant valueas well (1-103JK^kg"1). The volume ofthe air compartment (Vair) isequal tothevolume applied inthecomputation ofthecapacity for vapour and C0 2 (see Section 5.3.1 and 5.4.1). The canopy isthe fifth state variable in the thermal model. The net heatfluxto the canopy is defined by: H  can,net  =  R  UppCan + R LowCan + P VISCan + PNIRCan ~ H  t W m " 1(5-37)  CanAir - ^ a n C o v ~~ ^ a n S c r ~ ^ a n F l r ~ L CanAir  which leads to a rate of temperature change according to ^  =C a i i l A I H c a n , n e t  P ^ l (5.38)  The heat capacity of a square meter of canopy leaves (Capleaf) was estimated by Stanghellini (1987) at 1.2-103 JK-'m-2. The variable LAI defines the leaf area index, which is the total leaf surface per square meter floor surface. The floor and soil below the greenhouse represents a massive thermal capacity with apoorthermal conductivity. Thefloorofthegreenhouse isassumed toconsist of concrete tileswith athickness of 3cm. The combination of the large heat fluxfrom solarandthermal radiation andthepoorconductivity oftheflooryields  82  Thethermal sub-model alargetemperature gradient atthetopofthefloor.Thesurface temperature shows diurnalvariations ofsome 10°C.Tobeabletodescribethistemperature gradient thefloor hastobeconsidered inlayers.Therefore thetilesarerepresented bytwo statevariables, named Tnr and Tsol.Tnr represents thetemperature ofthetoppart of the tile, and Tsol describes the temperature at the bottom part. The top of the tilehasathicknessof 1 cmandthebottom hasathicknessof2cm.Thethickness ofthesecond floor compartment (Tsol) isallowedtobelargerbecausethegradient inthispart of the floor is much smaller than that at the top of the floor. The net heat flux to the floor compartment (Tnr) can be read from Figure 5.3 H  flr,net =  R  LowFlr + RUppFlr+ HAirFlr+ ^anFIr +  R  VISFlr + RNIRFlr ~  H  V^^  (5-39)  FlrSol ~~ RFlrScr ~ RFlrCov  The rate of temperature change asa function ofthe thermal capacity of the state variableandthenetheatfluxcanbeexpressed analoguetoforexampleEqn.5.28. The thermal capacity of the floor can be computed easily from thespecific volumetric heat capacity of concrete (2.0-106Jm3K"') and the thickness of the layer represented byTflr (1cm).Thenetheatfluxtothelowerpart oftheconcretetiles is governed by only twofluxes. Hsol)net = H FlrSol - H S o ] S o 2  [Win2] (5.40)  Because thevolume ofthe lower part of thetile is double the volume of Tflr, its capacity is twice the capacity of Tnr. The computation of the net fluxes to the layer i (i=2..6) of the soil is similar to Eqn. 5.40. HSo/,net = H S o / , ; S o ; - HSo,.So,.+;  [Wrn2] (5.41)  The thermal capacity of the soil layers below the tiles is determined by the thickness of the soil compartments and their volumetric heat capacity. The thicknesses of the soil layers below the tiles increases with the following sequence: thso2=0.04, thso3=0.08, thso4=0.16, thso5=0.32 and thso6=0.64 [m] (5.42) The increment ofthe layer thickness with an exponential sequence isto limit the number of state variables and still describe a gradient in a volume with a large thermal capacity. To compute the volumetric heat capacity of the soil it is assumed that the soil consistsof70%sand,20%waterand 10%air,holding for atightsandysoil.Thus the cubic heat capacity of the soil is defined by: P ^ r O ^ P C p ^ +O ^ p C p ^ +O.l pc pair = 1.73-106 [Jm-3K-'] (5.43) Of course, with pcpsand=1.28-106 and pcpwaler=4.18-106, the contribution of the heat capacity of air in pc pson is negligible. 83  Greenhouse climate simulation Finally,onbehalfofthecomputation ofthemeanheat lossfromtheheatingpipes (see Section 4.4.1.4) the net flux from the upper and lower heating circuit must be determined. From figure 5.3 these net fluxes read: H  upp,net = -( R UppScr + RUpPCov+  fWm'2] (544>  H  UppAir+ RUppCan+ RUppCrp)  and H  low,net = -( R LowScr + RLowCov+ H LowAir+ RLowCan+ RLowCrp)  t W m " 2 ] < 5 - 45 )  Thefluxesare signed negative to conform tothe other expressions for net fluxes in this section. However, in the expression for apip (Eqn. 4.7, page 37), the net flux from aheating pipe isconsidered a heat loss and therefore treated asapositive value.  5.5.2 Fluxes in the thermal model Inthethermalmodelconvective,conductiveandradiativeheatexchangeprocesses can be found. Moreover there are a number of forced fluxes to be defined. All fluxes, or the exchange coefficients by which the fluxes can be computed with equations such as Eqn. 5.1,5.2 or 5.3, are discussed in four separate sections.  5.5.2.1 Convective heat fluxes Inagreenhouse, convectiveheat exchangeplaysaroleatthevarious surfaces and by the ventilation process.  Heatfluxesat the surfaces Going from the top to the bottom of the conceptual greenhouse, the cover isthe firstsurface. Attheupperside,thegreenhousecover loosesheattotheoutsideair. Bot (1983)devoted asubstantialpart ofhisresearch tothedescription oftheheat exchange process at this saw-tooth surface. He found a satisfying description of the heat exchange coefficient as a function of the wind speed: ct=   f 2.8 + 1.2 Windsp I Windsp < 4 m s"1 OR i 1 2.5 Windsp 08 |Windsp > 4 m s'1  , [Wm"2glassK"1](5.46)  Because the tilted cover yields a cover/floor surface ratio larger than 1the heat exchange coefficient for the greenhouse cover to the air per m2 floor surface reads: 84  Thethermalsub-model HEC  [Wm-2K-'] (5.47)  CovOut = o/cos(i|>)  Theheatfluxfrom thecovertotheoutsideair (HCov0ul) canbecomputed withan equation analogue to Eqn.5.1. Attheinner sideofthecover,theheatexchangeprocess isconsidered tobedetermined by free convection from an inclined surface. Thus, referring to Appendix A(seeEqn.A.4),theheatexchangecoefficient attheinnersideofthegreenhouse cover is described by: a = 1.70 (cos i)/ ) 0 3 3 AT 033  [Wm^glassK'1] (5.48)  Indeed, thisvaluehas afair agreement withtheresultsmentioned by Bot(1983), whofound heatexchangecoefficients ranging from 2to4Wm"2glassK"'.Dependingonthestatusofthethermal screen,theheatfluxtothecovereither originates fromthetopcompartment, or from themain air compartment. However, theheat exchangeprocessisthesame.Thus,takingthelargersurface duetotheroofslope (i)/)compared tothefloorsurface intoaccountthefollowing relations arederived. HEC TopCov = 1.7 (T top - T c o v ) 0 3 3 cos(v)-0-66  [ W m ^ 1 ] (5.49)  T c o v ) 0 3 3 cos(y)-0-66  [ W m ^ 1 ] (5.50)  HECM^OV = 1-7 (T air "  Below the cover, the next solid surface assigned to a state variable is that of the thermal screen. Because theporosity of thethermal screen subject to thepresent work* isverysmall, thescreen canbeconsidered tobeahorizontalflatplatewith respect to convectiveheat exchange.Theheat exchangebetween the air below to the relative cold screen isan upward heat flux. The same holds for the exchange fromthe screen to the relative cold top compartment. The heat exchange coefficient for an upward heat flux to or from a plate is found from Eqn. A.4 (see Appendix A). Takingaccountofthescreenclosure(SC),theheatexchangecoefficients from the air to the screen and from the screen to the top are described by: HEC ScrTop = SC 1.7 (T scr - T t o p ) 0 3 3  [Wm-2K-'] (5.51)  HEC AirScr = SC 1.7 (T air - T s c r ) 0 3 3  [Wm"2K-'] (5.52)  SC iszerowhenthescreen isopened and 1 when itisclosed. However, tocarryoff moisture, incommon horticultural practice thescreen isoften opened slightly. In such cases the screen closure is 0.98. Working downwards through the conceptual greenhouse, the upper heating pipe isthenext solid element. The pipe is located in the free air above the canopy.In Appendix A, for such aheating pipe theheat exchange coefficient is determined "Thethermal screen applied in thiswork (LS-10+) is afilmstrip fabric. The fabric is capable of transporting moisture. 85  Greenhouse climate simulation at (see Eqn.A.6): a = 1.28 X ' 0 2 5 AT 025  [Wm"2pipeK"1](5.53)  with X the characteristic dimension of the pipe, which is its diameter. With the introduction ofthevariable lupp,denotingthelengthofupperheatingpipesperm2 floor surface andavariabledupp,beingthediameter ofthepipe,theheatexchange coefficient of the upper heating pipe for heat exchange with the greenhouse air can be expressed as: HEC UppAir = 1.28 Tid u p p 0 7 5 l upp (T upp - T a i / 2 5  [Wm-2K-'] (5.54)  If the lower heating pipe hung in free air, similar to the upper heating pipe,the variableH E C L , , ^ , couldbedetermined withanequation likeEqn.5.54.However, sincethe lower heating pipe is situated near the ground and closeto the canopy, theheat exchangeprocess is likely tobesomewhat hindered, compared toapipe in free air. Therefore, instead of the theoretical value, as applied for the upper heating pipe,the results of measurements of Bot (1983) are used to describe the heat exchangecoefficient. Thebestfitofhisresults for apipewith adiameter of 51 mm yielded a heat exchange coefficient described by: a = 1.99AT 032  [Wm"2pipeK"'](5.55)  Indeed, as long as the temperature difference between pipe and air does not exceed 75 °Cthis heat exchange coefficient is smaller than the value computed by Eqn. A.6. The full equation that expresses HECLowAir reads: HEC  LowAir = 1-99* d,ow l,ow (T |ow - T a i r ) 0 3 2  [Wm^K"'] (5.56)  where l!owand dloware defined analogue to luppanddupp. Thecanopyleavesarethefifthsolidsurface inthegreenhouse.Theexpression for the heat exchange coefficient at the canopy leaves was derived by the work of Stanghellini (1987).Byusingartificial leaves,shedetermined theboundary layer resistance to heat transfer as a function of micrometeorological quantities. For tomato leaves she found: rH =  • , n,<(' l T c r p - T A i r | + 2 0 7 u 2 ) 0 - 2 5  Ism J(5.57)  with rHthe boundary layer resistance for heattransfer (sm"1), t the characteristic dimension of a canopy leaf (the width) (m) and u the local air velocity (ms"1). Obviously thisrelation shows areasonable dependence ofrHon local air velocity and temperature excess of the leaf surface. In greenhouses,theairvelocities around theleavesare intherange of0.04to0.1 ms"1 and the temperature difference between leaves and ambient are limited to some 2 K(Stanghellini, 1987).With a mean width of the canopy leaves of 0.05 86  Thethermal sub-model mtheresistance toheat transport will vary between 200and350 sm"1. Rather than aresistance,the thermal model usesanexchange coefficient torelate aheatfluxtoatemperature difference. Athermal diffusive resistance canbeconverted toaheat exchange coefficient by(Monteith, 1973): a =  PcP,air/rH  [Wm"2leafK'1] (5.58)  With theresistance (rH) ranging between 200to350sm"1,a varies between 3.4 and6Wm'2K"'.Despitethesevariationthemodelusesafixedheatexchangecoefficientof 5Wm'2K"'.Theheatexchanging surface ofthecanopy istwicetheLAI because sensible heat isreleased attheupper andthelower side ofa leaf. Thus HEC canAirbecomes: HEC  [Wm^IC1] (5.59)  CanAir =2 LAI5  The last surface distinguished inthethermal model isthegreenhouse floor. The floor can be warmer or colder than the air above it. Since theNu-Ra relation differs forthesetwocases,theconvectiveheatexchangecoefficient isdetermined by either oftwo equations. With Equations A.4andA.5 from AppendixAandacharacteristic dimensionof 3 m, assuggested inAppendix A,theheat exchange coefficient isdefined by:  {  1 7 (T  — T -33 flr  025  1.3(T a i r -T f l r ) 0 - 2 5  Ij.  i  >  j. air  [Wm-2K-'] (5.60)  |Tflr<Tair  Ventilation Ventilation replaces greenhouse airbyoutdoor air.Inmost casestheexchangeis governed bynatural ventilation through windows, from whichtheaperture ofthe windowsiscontrolled bythe greenhouse climate controller.Asmall,uncontrollable,ventilation flux iscausedbyleakagesincegreenhousesarenotcompletely airtight. Thecomputation oftheairexchangeratefvent(m3m"2s"'), isbased ontheworkof De Jong (1990). Inhisthesis hedetermined arelation todescribe the impactof windspeed,temperature difference andopeningangleontheairexchangeratefor three window geometries. In hiswork, eachofthetwo main factors driving airexchange (temperature difference andwind) were studied separately andcombined afterwards. It appeared that thecombination could beperformed byavector-like summation. •window=( W +•wind')°"5  ^window's"'] (5.61)  The contribution oftemperature driven ventilation (<t>temp)inthetotal ventilation flux is small but can be important during nighttime and in winter. ^taap was 87  Greenhouse climate simulation described by: ^ternp= Cf//3( | gBAT | )"^>H 0.5 ul.5  [mV1window"1] (5.62)  The constant Cf accounts for the discharge of energy caused by friction in the windowopening.Inthework ofdeJong,itappeared tobe0.6 andwashardly affected by the window geometries subject to his work. / isthe length of the window (m), as depicted in Figure 5.4. g isthe gravitational acceleration (ms'2) and Bthe thermal expansion coefficient (1/283 K"1). H is the height of the front openingofthewindow(m) (seeFigure 5.4),expressed byH=/z(sin(n/)-sin(ij/-0)), with \i theroof slope, 8 isthe opening angle of the window. In the model, Eqn. 5.62 is applied on both leeside (<t>[emp,i)and windward side (<t>,emPjW)windows. To describethewind speed driven ventilation, deJongused 'Window Functions' that relate the air exchange rate through a window with the wind speed and the surface of the window (G=(j)/(A0 u), with u the wind speed (ms"1) at reference height (1.5 m) and A0the surface of awindow (A0 =lh)). The window function Gw(9)holdsforwindowsatthewindward sideoftheroof andGj(8) describesleeside ventilation.  gutter  Figure5.4 Window dimensions With the window functions, the air exchange rate is defined by: <t>wind = ((°l( e ) + G w( e ))A 0 "  [mVwindow-1] (5.63)  In deJong's measurements theventilation fluxes didn't appear to be affected by wind direction. Moreover, for small opening angles of the windward ventilators (0<12°), the experiments showed that windward ventilation could be considered asadditional toleeside ventilation. DeJong's work doesnotmention whether the windwardsideventilationcanstillbeconsidered additiveforlargeopeningangles. However, during the period of the year that the greenhouse is heated, the wind-  Thethermalsub-model ward sideventilators are hardly used. Thus,with respect to energy consumption, a possible (large) error inthe total ventilation flux if both windward and leeside ventilators are opened with large angles is not a serious problem. Forthedifferent window geometries studiedbyDeJong,thewindowswithanaspectratio(llh)of 1.825 showthemost resemblance towindows inthemostcommontypeofgreenhouse.Therefore thewindowfunctions thatweredetermined for that case are applied in the present model. These window functions read: G,(G) = 2.29-10"2(1 - exp(-Q/2l.)) 3  Gw(9) = 1.2-10" 0exp(0/211)  [-] (5.64a) [-] (5.64b)  Combining Eqns. 5.61,5.62, 5.63 and 5.64, and introducing a variable fr^ndow, denoting the number of windows per m2 greenhouse, the air exchange rate from the greenhouse air to the outside air can be described by: f  vent = '/2 frwindow (<tvind2+ ^temp.w + ' K e m p / )°' 5  [ r n V r n 2 ] (5.65)  Theterm Vi accounts for thefact that(j)^^ includestheair exchangethrough both leeside and windward-side windows, whereas A^^ow counts all windows in the greenhouse. For a common Venlotype greenhouse, fr^^^ is 0.078 m'2. Due to the air exchange, indoor air with a heat content pcpajr Tair (Jm"2m"3) is replaced by outdoor air with aheat content pcpairTout.Thus,when the difference indensity of inside andoutside air isneglected, theheatexchangecoefficient for heat exchange by ventilation, is determined by: HEC AiK)ut = pcp,air(fvent + ufleakage)  [Wm-2K-1] (5.66)  The termfleakagetakes account of leakage through cracks in the greenhouse construction. Obviously, the leakage is supposed to be linearly dependent on wind speed.  Air exchange through the screen Thedirectheatexchangebetweentheaircompartment belowandabovethescreen is dueto the exchange of air between thetwo compartments. The exchange rate is expressed as a volume flux per m2 floor surface (m3m"2s"'). Theairexchangeisbasedontwomechanisms.Inthefirstplace,air istransported through theopenings inthe fabric. Inthesecondplace,whenthescreen isopened a crack for dehumidification, air isexchanged through arelatively large opening. Inbothcasestheair exchange isinduced bypressure ordensity differences. Pressuredifferences originate from windspeedfluctuationsinducingpressure fluctuations inthetop compartment through opened windows or leakage.Adensity difference originates from a temperature difference across the screen. 89  Greenhouseclimate simulation Temperature-driven airexchangethrough fully closed screensisintensively studiedbyBalemans(1989).Hemeasuredtheairexchangeratethroughthescreen for 12different typesof fabrics asafunction ofthetemperature difference acrossthe material. Subsequentlyhefitted afunction ofthetypefscreen=K^AT066throughthe data,wherefscreenistheairflux through thescreen (m3m"2s'1), K,the 'screen flow coefficient' (m3m"2s"1K"066) and ATthe temperature difference across the screen (K). Table 5.1 lists some of his results.  Table5.1 Screen-flowcoefficientsfor various screenmaterials(extracted from Balemans,1989). Material type Knitted polyester Knitted polyester Woven polyester Film strip fabrics Non-woven  Trade name TD 55 TD 85 Verzuu GPA bandjes LS 11 Tyvec gold standard  K, (mWV'K" 0 -") 0.480-10'3 0.37210"3 0.203-103 0.161-10'3 0.243-10"3  If thescreen isopened slightly, theair exchange through this opening will dominate the air exchange through the screen. Unfortunately hardly any literature on thissubject couldbefound.However,recently Miguel(1995)presented atheoretical model on air exchange through a crack induced by density difference. His model isbased on theNavier-Stokes equation: 4>crack = P 9 (0-5 PmeanSO g ( p , - p 2 )) ° 5 ^mean  [ m V ] (5.67)  In this equation (|>crackisthe flux of air through the crack (mV1), L isthe length oftheopening inthescreen (m), SOthescreen opening(m), pmean themean density of air beneath and above the screen (kgm"3), gthe gravitational acceleration (ms'2), p, the density of air above the screen (kgm"3) and p2 the density of air beneath thescreen (kgm"3).The comparison of thetheoretical results and experimental data showed a good resemblance (Miguel, 1995). Also, a comparison of the results of the equation above with results from experiments on narrow, horizontal openings carried out by De Jong (1990) showed a good correspondence. In a Venlo type greenhouse screens are usually located between the gutters and extend from onesupporting element tothe next. InFigure 5.5 asketch ofathermal screen in a greenhouse construction is depicted. Combining the air flow through the screen with the airflow through the crack, a single equation can be constructed.  90  Thethermal sub-model fAirTop = SCK s AT°- 66 + J  5 2  [mVm- z ] (5.68)  (0-5PmeanWd-SC)g(p ajr - ptQp)) ° 5  InthisEquationfAirTop refers totheexchangerateofairbetweenthe compartment beneath andabovethe screen. SC isadimensionless number between 0and 1 describingthefractional screenclosure.ThevariableLhasdisappearedbecause<t>crack was divided by LxW. SO has disappeared, because it has been substituted by W(l-SC). For Ksa suitable value must be used from Table 5.1.  gutter  girder  Figure5.5Sketchof a screen construction. Theeffect of(windspeeddriven)pressure fluctuation onairexchangethroughthe screen andcrack iseven lesswellknownthanairexchangethrough thescreenby temperaturedifferences. However,incustomary greenhouseoperationthesituation wherescreensareusedandthewindows areopened occurswhentheclimatecontroller opensthewindows tocarry off aheatsurplus (duetoartificial illumination or aminimum pipe temperature) or to decrease humidity. Thusthe air exchange rate between the greenhouse air compartment through the crack to the top compartment and the outside air ispart of a feed-back control loop.This means that deviations between model and reality are strongly attenuated. Therefore, in this work no further attention is devoted to this case. Theheatexchangecoefficient from themain aircompartment tothetopcompartment can be stated analogue to Equation 5.66. HECAirTop  l ~ Pcp,air p.airfAi AirTop  [Wm-2K-'] (5.69)  91  Greenhouse climate simulation 5.5.2.2 Conductiveheat fluxes Inthemodelpresented, conductionplaysaminorrole.Onlytheheatexchangebetween the soil layers istreated as a conduction process.The general equation for one-dimensional conduction reads: <t>" = - X g  [WnV2] (5.70)  Where<)>" istheheatfluxdensity(Wm"2K"'),Xthethermal conductivity (Wrn'K'1) and dT/dx the temperature gradient (Km*1). The negative sign expresses that the (positive) direction of the heat flux is opposite to the temperature gradient. Indiscretesimulationmodels,thecontinuousgradient isreplacedbyatemperature difference. To do so, the continuous conducting medium is split up into several discrete compartments andthegradient isdiscretized bydividing thetemperature difference between the compartments by the distance between the centres of the compartments. Then the equation becomes: H = £ (T, - T2)  [Wm-2] (5.71)  where H isthe conductive exchange (Wm"2), d the distance between the centres ofthetwo heat exchanging compartments (m) and T,-T2 thetemperature difference (K). The term Xfdcorresponds with a heat exchange coefficient as applied in Eqn.5.1. The distances between the centre of the floor compartment and the first soil compartment is 1.5-10"2m(see Eqn. 5.42,page 83). Withthe thermal conductivity of concrete (1.7 Wnr'K"1) the conductive heat exchange coefficient between the floor and the first soil layer (HECFlrSol) can be computed easily. The heat exchange from the first soil layer to the second (HSoISo2) is partly governed by conduction through concrete, and partly by conduction through the soil.Toaccount for adifferent thermal conductivity, amean conductivity isused. This mean conductivity iscomputed from thereciprocal oftheweighed mean of l^concreteanc* 1^-soii-The weighing factors are the fractional contribution of the different constituents in the distance between the centres of the compartments under consideration. Althoughtheconductivity ofasoilwillvary considerably between soiltypes,and depends strongly on water content, thepresent model applies a constant value of 0.85 Wnr'K."1,which isderived from Houter (1989). Using the layer thicknesses mentioned in Eqn 5.42 the weighed mean thermal conductivity of the media comprising the second and third soil layer is 1.02 Wm"'K"'. Withthethicknessesoftheother layers (Eqn. 5.42),whichareallmadeupentirely of soil, the conductive heat exchange coefficients HECSo2So3 up till H E C ^ ^ can be easily computed. 92  Thethermal sub-model To determine theheat lossfromthebottom soil layer, represented byT ^ , tothe boundary variable in the soil (T^), half the thickness of the sixth soil layer is applied as the distance across which the temperature gradient is discretized.  5.5.2.3Radiativeheat fluxes Radiation is an important heat exchange mechanism. With respect to the present greenhouseclimate simulation modeltworadiative fluxes indifferent wavelength regions are important. The first is short-wave radiation, which acts as a forced energyfluxonthegreenhousesystem.Therefore, short-waveradiationisdiscussed in Section 5.5.2.4. Thesecond is long-wave radiative heat exchange inthewavelength region between 5and 50 urn. Long-waveradiativeheatisexchangedbetweenopaquesurfaces inthegreenhouse and between the greenhouse cover and the sky. The opaque surfaces are those from thecover,thescreen,theheatingpipes,thecanopyandthefloor. Thusthere are22radiativeheatfluxes tobedetermined (6+5+4+3+2+1 insidethegreenhouse and for theradiation from the cover tothe sky). The surface temperatures ofthe heat exchangingbodies,theemission andreflection coefficients inthe long-wave band, and the mutual view factors play a role in this computation. Going from thetop downwards through the conceptual greenhouse, the radiative heat exchange between sky and cover is the first to be defined. The sky is assumed to radiate as a black body. Its (virtual) temperature (Tsky) is one of the boundary conditions inthemodel and ispassed tothemodel bytheweather data. Of course a measured value for Tsky is preferred, but when asky temperature is missing in set of weather data, the sky temperature can be estimated from other meteorological quantities by an approach presented in Appendix F. From Appendix E, the equation describing the radiative heat exchange between cover and sky reads: RcovSky = ecov(up F CovSky A cov CT ( T c o V 4 ~ T sky 4 )  t W m ' 2 ] <5-75)  The emission coefficient (e) isgivenanextra index(up) because for coated cladding materials, the emission coefficient of upper and lower side of the material can be very different. Due to thetilted greenhouse cover the view factor FCovSky issmaller than 1.However, theproduct FCovSky-ACovis 1 becausethesky encloses the greenhouse cover. Thus equation 5.75 reduces to: RcovSky- W  ° <Tcov4 " Tsky4>  [WmJ] (5.76)  To shorten the expressions presented, the radiative heat exchange processes are referred tobytheirexchangecoefficient ratherthanbythedescription oftheheat flux. Usingtheconventionspresented inSection 5.2.3 (Eqn. 5.2 inparticular) the radiative heat transfer coefficient from the cover to the sky is defined by: 93  Greenhouse climate simulation [Wm- 2 Kl (5.77)  REC CovSky = sC0Vup a  For ordinary glass sC0Vup is 0.84 (Out & Breuer, 1995). The lower side of the cover faces thescreen, when itisclosed, or four other surfaces inthegreenhouse, when the screen is opened (the surface of the upper and lower heating pipe, the canopyandthesoil).Whenthescreen ispositioned somewhere between bothextremes, all five surfaces exchange thermal radiation with the cover. In that case the computation of view factors isvery complex. However, to reduce this complexity, and without making severe neglections because the screen ishardly ever in a position far away from the extremes, the view factors between cover and other bodies are supposed to be linearly dependent on the screen closure. The radiative heat exchange between cover and screen is computed by the linearized equation for radiative heat exchange (see Appendix E), since the screen temperature isdetermined byanalgebraic equation (seeEqn. 5.34).Thustheheat flux is determined by: scr cov.do ScrCov scr RSCICOV -— 1 1- D o Fe r^ F ^ r «.  A—T 4<T T  PscrPcov,do ScrCov CovScr  3/T T  rw.v,-2i /« HQ m <Tscr-Tcov) t W m 1(5-78)  The cover occupies all of the upper hemisphere of the screen. Therefore FScrCov equals 1.However,theradiating surface ofthescreen depends onitsclosure,and thus Ascrequals SC(the fractional screen closure). Tmisthemeantemperature of T^, and Tcov (K). The most convenient way to determine the view factor from cover to screen, required in the denominator, is using the reciprocity theorem (Pitts, 1986): F  ScrCov A s c r = F CovScr A cov "* F CovScr = F ScrCov A scr / A cov  H (5-79)  Because of the tilting roof pane, the radiating cover surface (Acov) is l/cos(y). Thus,FCovScr equalsAscrcos(ij/). The screen surface (Ascr)equals SC.Becausethe screen considered is not aluminized, the emission coefficient will be close to 1. Together with the low reflection coefficient of the glass(pCOv,do=l"ecov,do=0.16), the denominator in Eqn. 7.78 will be close to 1. Therefore, this denominator is omitted.After substitutionofFScrCovandAscrthelinearized radiativeheatexchange for the heat exchange between cover and screen is found. This reads: HEC  S c r C o v = e scr W d o  S C V  * ( T scr + T C 0 V ) 3  [ W i ^ K " 1 ] (5.80)  When the screen is opened, the cover faces the upper heating pipes, the canopy and,through the spaces incanopy,the lower heatingpipes and the floor. Tocontribute tothescreen,allexpressions for theradiative exchangeprocesses from the cover tothebodiesbeneath thescreen arepremultiplied by(1 -SC). Thustheradiative heat exchange between cover and upper heating pipe is described by:  94  The thermal sub-model  R E C U p p C o v = ( 1 -SC) E up P e cov.do F UppCovAu pp CT uppcov !_ p u p p P c o v > d o l-U p p C o v i - CovUpp  Theview factor of an infinitely longpipetoaninfinite cover is0.5,sincehalfthe hemisphere around thepipe islocated abovethepipe.However,theupper heating circuit consists of a network of parallel pipes. Thus, a small part of the hemisphere of a heatingpipe isoccupied bytheneighbouringpipes.From theworkof Sparrow and Cess (1970) it can be derived that the view factor of a pipe with a diameter of 0.051 mto aneighbouring pipe onthe left and onthe right side at a distant of 1.6 mis0.01.Therefore, afraction 0.005 oftheupperpart ofthehemisphere is occupied by the neighbouring pipes. This is such a small fraction that it can be neglected. Thus theview factor of the upper heating pipe tothe screen (FUppCov) i s °- 5  Using the reciprocity theorem, FCovUpp can be defined by FCovUpp = FUppCov Aupp/A^y.With Aupp being about 0.1,FCovUpp becomes about 0.05. The emission coefficient of heating pipes (white painted) is about 0.88 (American institute of physics handbook, 1972).Thus, pupp is about 0.12. With the small values in the multiplicative term in the denominator of Eqn. 5.81 it is obvious that the denominator can be omitted yielding: REC UppCov = (1- SC)0.5e upps covdoI upp*d uppa  [ W m ^ ] (5.82)  The next opaque element of the greenhouse construction inthetop-down view is the canopy. In general terms the radiative heat exchange coefficient between the cover and the canopy is analogue to Eqn.5.81. R E C C a n C o v = (1-SC)  ^nWdoFCanCovAcana 1 Pcan Pcov,do **CanCov ^CovCan  ^ - 2 ^  (5 83)  Becauseboth reflection coefficients inthedenominator areclosetozero,andthe view factors aresmallerthan onebydefinition, asimplification of the relation by a denominator equal 1is allowed. Theviewfactor forradiation between canopyandcoverisdetermined byapplication of the reciprocity theorem on the view factor for radiation from cover to canopy.From thepreviously defined viewfactor from upperheatingpipetocover (0.5) the view factor from cover to pipe can be computed using the reciprocity theorem.Foranendlesscover,FCovUppcanbecomputed tobe0.5nduppluppcos(y). Thus, by definition, the hemisphere occupied by the other opaque elements beneath the upper heating pipes is stated by (1-0.5 n dupplupp)cos(j/). Since the radiativeexchangetakesplaceatobstructingcanopysurfaces,theviewfactor from the cover tothe canopy can bedetermined by the fraction of the hemisphere not masked by the heating pipes which is occupied by the canopy. This fraction is related to the leaf area index by multiplication of the LAI with the long-wave extinction coefficient inanexponential function (seeAppendixD). Thustheview 95  Greenhouse climate simulation factor ofthe cover tothecanopy becomes F  CovCan= 0 "° 5 *<W*^ V-exp(*LAI))cos(V)  [-] (5.84)  where k,isthelong-wave extinction coefficient. Theview factor FCanCov can be found from thereciprocity theorem yielding F  CanCov= FCovCanAcov/Acan H ( 5 - 85 ) The radiating surface ofthe canopy stand isvery large (twicetheLAI) butmost thermal radiation is re-radiated within the stand. Thus an effective radiating surface mustbedetermined. This surface isdescribed bythe integral ofthelongwave extinction function (Stanghellini, 1987). A can = 1 - expi-k, LAI)  [m2] (5.86)  After combining Eqns. 5.84,5.85and5.86,andstating that Acov=l/cos(ij/), the view factor from canopy tocover appears to be F  CanCov = ( 1 ~ 0.57tdupplupp)  [-] (5.87)  Combining Eqn. 5.86 with the simplified equation 5.83 the radiative heat exchange coefficient between canopy andcoveris: RECCanCov=(l-SC) e can e cov , do F CanCov (l-^(-k,LAI))a  [ W m ¥ ] (5.88)  The emission coefficient of the canopy (scan) istaken tobe 1,meaning thatthe leaves areconsidered asblack bodies (Stanghellini, 1987). The fourth opaque surface beneath thecover isformed bythe pipes ofthe lower heating circuit. Just likethereasoning applied inthe definition ofRECCanScr,the view factor forradiation from thecover tothelower heating pipe isdetermined by thecomputation ofthe view factor for radiation from thelower heating pipe tothe cover. Todetermine thelatter itisrecalled thatthe simulation model conceptualizes that thelower heating pipe 'sees' five opaque surfaces. These are the floor, theneighbour pipes, thecanopy, theupper heating pipes andthecoveror screen.Bydefinition thesumoftheseview factors isone.Thus,themost convenient waytodetermine themost difficult view factor istocompute theothersand to consider themost difficult oneastherest factor. Theviewfactor totheneighbouringpipescanbecomputedwiththeformulas presentedby Sparrow andCess(1970).Itappears thatFLowLow isabout0.02.Accordingtothesame reasoning asinthediscussion onRECUppCov, itcanbestated that F LowFir e q u a ' s 0.49.If there isnocanopy, theview factor for radiation from the lower heating pipe totheupper heating pipe is about 0.005. This fraction is alreadysmall andbecomesevensmallerwhenthecanopyhasgrowntoacertainextent.Therefore theradiation exchangebetween theupper and lowerheatingpipes isneglected. Consequently, without acanopy,theview factor from pipe tocover equals 0.49. Becausethe canopy obstructs theexchange withthecover, theview 96  Thethermal sub-model factor for the heat exchange between lower pipe and cover becomes F  LowCov= 0 4 9 exP('k L A I ) ["] (5-89> Thedenominator inthe full equation ofthetypestated inAppendixEasequation E.11isclosetoone.Thustheradiative heatexchangebetween lowerheatingpipe and cover can be stated as: RECLOWCOV= (1-SC) e, ow eCov,do*  d  lowW  FLOWCOV°  tWm^K"4] (5.90)  With Fj^^oy stated by Equation 5.89. The emission coefficient of the lower heating pipes (elow) is equal toeupp. The last opaque element exchanging radiation with the cover is the floor. The floor 'sees' thelowerandupper heatingpipes,thecoverandthecanopy.Tocomputetheview factor from the floor tothecover, theabsence of acanopy isagain assumed first. A part of the full hemisphere ofthe floor ismasked by the lower heatingpipe.This part isexpressed by 0.497idlowllow.Theremainder ofthehemisphere is either empty, obstructed by the canopy or obstructed by the upper heating pipe. Thus the view factor from floor to cover is determined by: ^FlrCov = 0 - ° - 4 9 *<Wlow) ^ ( " k l L A I > (1-0-5 *<Wupp>  U  (591)  Because the canopy occupies a large part of the hemisphere of the floor for the major part of the year (resulting in a low view factor to the cover), and the reflection coefficient of the cover for long-wave radiation is low (about 0.1), multiplereflections arenegligible.Therefore theequation describingtheradiative heat exchange coefficient does not contain the extensive denominator. REC FllCov =(1-SC)Eflr E covdo F F I l C o v a  [Wm-2K1 (5.92)  The emission coefficient of the floor, consisting of concrete tiles, is assumed to be comparable to that of brick. For brick an emission coefficient of 0.89 was found (American institute of physics handbook, 1972). Thenextopaqueelement forwhichtheradiativeexchangeprocessesaredescribed isthethermal screen. Because it'stemperature iscomputed byanalgebraic equation, all fluxes are linearized. The radiative exchange coefficient between screen and cover was already stated in Equation 5.80 Becauseinallpreviously derived radiativeexchangecoefficients thecoveractsas a horizontal surface, from geometrical point of viewthe closed thermal screen is comparable to the cover. Thus the expressions for the heat fluxes are similar, exceptthat theterm (1-SC) must besubstituted by SC.Moreover, because ofthe algebraic solution forthescreentemperature requires linearexchange coefficients all expressions for the radiative heat exchange with the screen are linearized.  97  Greenhouse climate simulation HECUppScr=SC0.5E ^ e ^ n d ^ p p '/2a(Tupp+Tscr)3  [ W m ^ 1 ] (5.93)  HECCanScr=SC8canescrFCanScr(l-e-klLAI ) '/2a(Tcan+Tscr)3  [ W m ^ 1 ] (5.94)  H E C ^ ^ =SCeloweiajrdlowlIowFLowScr '/2a(Tlow+Tscr)3  [Wm"2^1] (5.95)  HECnrScr =SCeflr 8scrFFlrScrV,o{l^lJ  [Wm^K"1] (5.96)  The view factors FCanScr,F^s,.,. andFF)l.Scr are equaltoonespreviously defined as Fcancov ^ W o y  and F  n^ov respectively.  The next opaque element in the greenhouse isthe upper heating pipe. From this element two of the heat exchange processes (Ruppc0v a n d R-uppScr) w e r e already defined. To compute the heat exchange between upper heating pipe and canopy, it isrecalled that a fraction 0.5 ofthehemisphere around theheatingpipe is considered to face downward (seethediscussion onRECUppCov). Part ofthat fraction isoccupied by canopy leaves.Thustheview factor for radiation from theupper heating pipe to the canopy is defined by F  UppCan= ° - W ( - k l L A I )  H(5.97)  Withthisview factor, andgiventhefact that multiple reflections between canopy and pipe are omitted because the canopy ispractically black, the expression for the radiative heat exchange coefficient becomes RECuppCan= ^upp^can^UppCan*<Vu P P«  [Wm^K"4](5.98)  Thenextsolid surface belowthecanopy leaves iscomposed ofthe lower heating pipes.However, radiation exchangebetween theupper and lower heatingpipesis not included inthemodel because,evenwhen there isnocanopy,theview factor from the upper tothe lowerpipe isonly about 0.01. When thecanopy has grown to a certain extent, the view factor becomes even smaller. The flux tothe floor surface isthe lastradiative heat flux from theupper heating pipe that has to be defined. Taking into account that the canopy and the lower heating pipe mask the floor surface, the view factor of the upper heating pipeto the floor is defined by FuppFlr = °- 5 O-Kdiowliow)«P(-k|L A I ) ["I(5-99) Againthedenominator intheextensivedefinition oftheradiativeexchange coefficient is close to one. Thus remains: RECuppp,, = Euppe sol F U p p F l r 7tduppIuppa  [Wm^K"4] (5.100)  Forthecanopy,thefourth opaqueelement inthetop-down approachtothegreenhouse construction, the majority of radiative fluxes have already been described. Only the radiative heat exchangewith the lower heating pipe and the floor have 98  Thethermal sub-model to be defined. Due to similarity of configuration, the upward radiation from the lower heating pipetothecanopy isdescribed bythesametypeofequation asthedownward radiation of theupper heating pipetothe canopy. Thus, analogue to Eqn. 5.98,the radiative heat exchange between lower heating pipe and canopy is described by RECLowCan = elowecanFLowCan' " W l o w °  [Wm^K"4] (5.101)  The view factor F^^,,,, is defined by: F  LowCan = ° - 4 9 0 ~ exP^  LAI  »  H (5-102)  Theexpression fortheradiativeheatexchangecoefficient betweencanopyandsoil is derived in the same way as the expression for RECCanCov. RECcanFlr= W W 1 " 0 - 4 9 " ' W l o w X 1 - ^ ' L A I ) a  [Wi^IC 4 ] (5.103)  Thefinalradiative heatexchange coefficient tobedetermined describes thethermal radiation exchange between the floor and the lower heating pipes. This exchange process is similar to the heat Ruppcov Thus, analogue to Equation 5.82: RLowFIr= 0-49 e low ESO1 7tdlowl,ow o(T low 4 - T s o , 4 )  [ W m ^ 1 ] (5.104)  5.5.2.4Forced /luxes In the thermal model the forced fluxes originate from short-wave radiation and from latent heat associated with condensation and evaporation.  Short-wave radiation The short-wave radiation towhich a greenhouse isexposed originates almost exclusivelyfromthesun.Sometimes additionalshort-wave radiation isgeneratedby artificial illumination. Compared to the yearly energy content of solar radiation, the contribution of artificial light is very small but nevertheless, during winter, additional lighting can have an important impact on actual canopy growth and development and on the actual greenhouse energy budget. Solar radiation to which the greenhouse is exposed, contains wavelengths in a band between 0.3 and 3 urn. This wavelength band can be split in three spectral parts.Thefirstpart isUltraviolet (UV),ranging from 0.3-0.4 urn.The othertwo arevisiblelight,ranging from 0.4-0.7 urnandtheNear Infra Red(NIR), consistingofwavelengthsbetween 0.7and 3urn.Thevisible lightcorresponds withradiation of interest for biological growth. ThefractionUVisbetween6and 10%andvisiblelightcontributes for 45to60%  99  Greenhouse climate simulation totheintensityofradiation(Coulson, 1975).However,forplantgrowthmodelling purposes it iscommon usetoneglect these variations andtoassign 50%ofthe solar radiation tovisible light.Eventhefraction UVisgenerally neglected sothe other 50% isattributed toNIR (Monteith, 1973). Besidesthespectral division,solarradiationcan bedivided intodirectand diffuse radiation. Principally, direct radiation reaches the earth surface with a certain angle ofincidence, given bysolar position. This anglevaries during theday and seasons.InAppendixJanalgorithm ispresented that expressestheangleofincidence ofsolar radiation asa function oftime, latitude andlongitude. Diffuse radiation isomnidirectional andhasadistribution function fortheintensity ofradiation over thehemisphere. Intheliterature several distribution functionscanbefound (Coulson, 1975;Morris andLawrence, 1971).Inthisstudythe standard overcast skyisapplied (seealso Appendix C). Direct anddiffuse solar radiation areconsidered tobetwosets of input data. In themodel, solar radiation inducestheforced fluxes PSunCov, PSunAir>^sunCananc* PSunF]r. The heat flux PSunCov contributes to the absorption of radiation bythe covering structure. This flux isassumedtobelinearly dependent onthe intensity of solar radiation. PSunCov = *cov ddif + W  [Wm-2] (5.105)  The absorption coefficient ofthe construction wascomputed bythelight transmission model described inAppendix C.Fordirect radiation thiscoefficient was about 0.04 andslightly affected bysolar elevation andazimuth. From the diffuse radiationtowhichthegreenhouse isexposed also4%wasabsorbed bythecover. The present model discards thesmall variations ofacov. Solar radiation that hitsthegreenhouse cover andwhich isnotabsorbed by the cover iseitherreflected backtothe atmosphere ortransmitted through the cover. For direct radiation, thetransmitted fraction depends strongly on elevationand azimuth. Themodel presented inAppendix C calculates thistransmitted fraction. In theAppendix an example is given of transmission data for a modern Venlo type greenhouse. Intheequations inthis work thetransmissivity oftheconstruction for direct radiation isreferred tobyTdir. Thediffuse transmissivity canbecomputed from thedirecttransmissivity after the definition ofthe distribution function for the intensity ofradiation from the sky vault.Assumingastandardovercastskyandadoptingthecomputed datafordirect transmissivity, yieldsadiffuse transmissivity of0.79(seeAppendixC).Thetransmissivity for diffuse radiation isdenoted byxdif. However, after passing the covering structure, quite a lot of light obstructing elements arepresent within theenclosure. Here onecanthink of girders, luminaries, energy screen packages, feet etc..Thefraction oftransmitted light intercepted by those obstructions is denoted aobs.Eventually, this absorbed radiation 100  Thethermal sub-model willbereleasedtothegreenhouseair.Therefore aforced flux PSunAirisintroduced reading: P  SunAir = W W * d i f + 'dir ^dir>  [Wm" 2 ] (5.106)  Obviously, by applying xdif and tdir, aobs acts on the transmitted fraction of the solar radiation. In the present model aobsfor a greenhouse without a screen and without artificial illumination isassumed tobe0.06.Athermal screen isassumed to increase thisvaluewith 0.04, and the luminaries of artificial lighting intercept anadditional portion of 0.02.Theamount of light that ispassed bythecoverand not obstructed by construction elements in the greenhouse is either absorbed by the canopy, absorbed at the floor or reflected. The absorption of solar radiation by a canopy stand is discussed thoroughly in the thesis prepared by Goudriaan (1977). He showed that the absorption can be expressed by an exponential function of the LAI. It appears that the absorption of direct radiation differs from diffuse radiation. This difference is expressed by defining extinction coefficients for both diffuse and direct radiation. Besidesthe distinction between diffuse and directradiation,theabsorption ofNIRdiffers significantly from theabsorptionof visible light. Thus, the model computes two short-wave fluxes to the canopy, defined by: P  VISCan = (Idif<1-aobs)Tdif+PAluVIs)aCan,Vdif +I  P  dir T dir( 1 - a obs) a Can,Vdir  NIRCan = O d i f C K b s ^ d i ^ A l u N I R ^ a n j f d i f +I  I Wm " 2 ] (5-107>  [ W m ' 2 ] (5-108>  dir T dir(1_aobs)aCan,Ndir  In the equations artificial illumination (denoted by PA|uVis ^ d PAIUNIR) *Streated as diffuse radiation. These fluxes are defined in the last part of this Section. Thebackground ofthecomputation ofthe absorption coefficients for diffuse and direct VIS and NIR (acidic acan,vdir> acan.Ndif a n d ^c^Ndir respectively) is presented in Appendix D. It appears that for a common greenhouse canopy they can be expressed as: a  Can,vdif= ( ° 9 5 - °- 9 e*/>(-°-85L A I »  a  Can,vdir= (°- 9 4 " 0 9 5 exrt'k  LAI  » with k=0.88+2.6exp(-0.18 P)  [-] (5-109) ["]<5-110)  101  Greenhouse climate simulation a  Can,Ndif= ( ° 6 5 - ° 6 5 «/K-0-27LAI)  [-] (5.111)  a  [-] (5- 112 )  Can,Ndir=( a -  b ex  P('k LAI > with a=0.67 - 0.06ex/?(-0.08 p) b=0.68-0.50exp(-0.11p) k=0.25+0.38exp(-0.12 p)  In Eqns. 5.110 and5.112 Prepresents thesolar elevation angle. Radiation that isnot absorbed norreflected bythecanopy isabsorbed atthefloor ofthe greenhouse.This absorbtion wascomputed with themodel outlined inAppendix Dbyregistering the amount ofradiation notabsorbed bythe canopyand not reflected back tothe greenhouse ambient. This amount, must beabsorbedby thefloor.Byassuminganshortwaveabsorbtion coefficient ofthefloorof0.25for VIS and 0.6 for NIR, the following relations as a function of LAI and solar elevation angle were found. aFh.Vdif=ex/>(-0.92LAI) a  FIr,vdir = exP(-k  LAI  >  [-](5.113)  with k=  ° - 9 0 + ° 8 3 exp(-0A2 p)  [-] (5.114)  a  Flr,Ndif= ( ° 0 5 + °- 9 1 *xp(-0.50 LAI)  [-] (5.115)  Flr,Ndir = <a+ b exP(-k  H (5-116)  a  LAI  )  with a=0.05+ 0.06ex/?(-0.08 P) b=0.92-0.53ex/7(-0.18p) k=0.48+0.54eop(-0.13P) again with p the solar elevation angle. The absorption coefficients defined in equations 5.113till 5.116 canbeused inequations like 5.107 and5.108 toyield PviSFIr  anC  * PNIRFIr-  Theupward reflections ofthecanopystandandthereflections atthefloorthatare notintercepted bythecanopyarepartly intercepted byobstructing elements inthe greenhouse, partly reflected back tothe canopy andfloor,butforthe major part are scattered backtotheatmosphere.Because the intercepted fraction isnotmore than some 30%ofthe already small reflections this secondary intercepted radiation isneglected.  102  Thethermal sub-model Latent heat fluxes Within the thermal sub-model the latent heat fluxes are treated as forced fluxes because their magnitude is determined by the water vapour sub-model. In the thermal model there are four latent heat fluxes. These fluxes are computed by: „-2i  LlopCov = W MVjopCov  t W m 1 <5-J17>  L  ScrTop = A// MV ScrTop  [Win2] (5.118)  LAirScr = A"MV A i r S c r  [Wm"2](5.119)  LCanAir = A"MV C a n A i r  [Wm"2](5.120)  with AH the heat of evaporation (2.45-106Jkg"1).  Sensible heat lossfrom luminaries The electric power consumed by luminaries of the artificial illumination is only partly converted to short-wave radiation. Typically, 17%of theelectric power is converted toNIRand25% isconverted tovisible light(Philips, 1990).Thus,58% of the electric power is exchanged to the greenhouse by means of convection or by long-wave radiation. To contribute to this energy input a variable PAluAir is introduced. The definition of this variable simply reads: PAluAir=frSenAluPArtif  [Wm'2] (5.121)  inwhichfi^nAi,,isthe fraction ofthe electric power not converted to short-wave radiation. P ^ f denotes the electric power uptake of the artificial illumination (Wm'2). It is clear that PAiuVis a n d PAiuNir a r e calculated analogue to P A I ^ .  103  Introduction  6 RESULTS 6.1 INTRODUCTION  As stated inChapter 3,theprimary energy consumption of a greenhouse isaresult of the interaction between heating devices, requested greenhouse air conditions, properties of the building and greenhouse climate control. In Chapter 4 and5atooltodescribetheseinteractionswasdeveloped,comprising anintegrated simulation model of greenhouse climate conditions and the greenhouse heating system. In thischapter, first the quality ofthesimulation model to describe the dynamics of the greenhouse climate, its climate control actions and energy demand isdemonstratedbymeansofcomparisonsbetweenmeasurementsandresultsofsimulations.After the quality of the model has beenproved, thetool developed isused tostudyenergyconservingmeasures.Inthisstudy,theusualprocessofcultivating tomatoes serves as a horticultural context.  6.2 COMPARISONS BETWEEN SIMULATION MODEL AND MEASUREMENTS.  Aresearch facility attheIMAG-DLO sitewasusedtotest and adjust thesimulation model. In this facility measurements were carried out on aggregated greenhouse air conditions (air temperature, humidity and C0 2 concentration), control actions(windowapertures,heatingpipetemperatures,screenpositions,C0 2supply and illumination), and required heating power. Moreover, data on daily water consumption were gathered. Althoughthenumberofmeasured entitieswaslimited,thelong-term character of the measurements (some years) generated a vast amount of information on the dynamic behaviour of the greenhouse climate, its controller and heating system. In this section, first the experimental set-up is described, followed by the parametrization ofthemodelthatcorrespondstothegeometry oftheresearch facility. Thereafter comparisons of small time scale measurements (10 minute mean values) are made over a short period (three successive days). Comparisons spanningalongperiod (yearround)aremadewithlargetimescalemeasurements (daily averages). Finally some concluding remarks are made.  105  Results 6.2.1 Experimental set-up Tocomparemodel computationswithexperimental data,thefirstcompartment of the research facility has been used. A sketch of the floor-plan of the facility is presented in Figure 6.1.It can be seen that the facility comprises four compartments of 192 m2 each. In Figure 6.2 a cross-section through a compartment is shown. The research facility is a Venlo-type greenhouse with a roof slope of 25° and a gutterheightof5m.Twelveventilatorsweremounted intheroof(6attheleeside and 6atthe windward side of theroof segments). Thus,the number of windows per m2 greenhouse area(frwindow inEqn. 5.65) was 12:192= 0.0625.The ventilators were 3m wideand 0.86 mhigh, making thearea of a window 2.64 m2(A0 in Eqn. 5.63). Fully opened, the window pointed 5° upward. The leakage of the compartments (f|eakagein Eqn. 5.66) was estimated on 1.5-10"4nvWV/Xms"1).  r  _. "  i  ir  "v  2000 m_ path  heat storage tank * ~ 9 6 0 m ~*  (6  o  o  corridor  o  Figure 6.1Floorplan of theresearchfacility. Inthecompartments, roseswere grown onmovablebenchesjust abovethelower heating pipes. Because the benches were movable, practically the entire floor of the growing area was occupied by the canopy. The path at the head of the compartment occupied 10% of the floor surface. The benches consist of a pair of translatable girders carrying small gutters, which were positioned perpendicular on the girders. Thus the benches have an open structure. The gutters support rockwool inwhich theroses are rooted. The roseswere planted inJanuary 1992. Allmeasurements applied inthecomparisons are from February 1993orlater, so in all simulations the canopy in the greenhouse is considered to be a full grown rose stand.  106  Comparisons between simulationmodeland measurements  artificial illumination upper distribution circuit movable benches lower distribution circuit Figure6.2Cross-section of a compartment. From mid-August to the end of April supplementary lighting was applied in the first and fourth compartment. With 16 SonT-Agro luminaires in each compartment, and the electric power demand of the lamps being 475 W, the electric power demand was 44 Wm'2 the intensity of shortwave radiation to the canopy was 11Wm"2.Duringnighttime,thelampswereswitched on,5hoursafter sunset. Duringdaytimethelampswereonwhenthe(outside) intensity ofglobalradiation dropped beneath 75Wm"2.When on,the illumination was switched off onehour before sunset to imply a natural dusk. Thecompartments wereheatedwithtwoheatingcircuits.Thelowerheatingpipes consisted of6heatingloops,eachwith alength of42mandpositionedjust above the floor. The pipes had a droplet shapeand had awet cross-section of6.25TO"4 m2(thevariable %7tdin2inSection4.4.1.1).Documentation onthispipingmaterial reports the heat exchange coefficient of the pipe to be comparable to the heat exchange coefficient of acircular pipe with a diameter of 51mm (van Leeuwen, 1992). Thus, with respect to heat exchange processes, the lower heating pipe is treated likea51mmcircularpipe.The flow throughthelowerheatingcircuitwas 1.9 m3per hour. The lower heating pipes acted as the primary circuit. The upper heating pipes were hung at a height of about 2 meters and only used duringperiods with ahighheatdemand. Theparameters ofthissecondary circuit were already described in Section 4.4.1.2). Toallowfor adetailed comparison between model andexperimental datathesensorswerescanned every twominutesand,after averaging 5samples,stored as10 minute mean values in daily datafiles. With respect totheoutsideweather conditions the air temperature and humidity, virtual sky temperature, wind speed and 107  Results intensity of global and diffuse solar radiation were measured. The wind direction was registered, but not stored since this quantity is not required in the present model. Inside the greenhouse, temperatures and humidity and C0 2 concentration of the airweremeasured. Thetemperature measurements comprised theairandthesupply and return temperatures of both heating circuits. From the heating circuits, alsotheheatdemandwasmeasured. Furthermore theheatproduction oftheboiler andtheheatproduction associated withcarbon dioxidesupply andcombined heat and power was measured. Finally, information on climate controller output on window apertures, the position of the thermal screen, the status of artificial illumination and the amount of C0 2 artificially supplied to the greenhouse was stored. To overcome scaling problems related to the small dimensions of the research facility as compared to horticultural practice, the boiler was implemented by a hardware simulation by means of valves that control a hot water supply to the heatingsystemofeachresearch compartment. Also,thecombined heatandpower of the research facility was not a real engine, but implemented by a hardware simulation by means of a heat exchanger. The heat associated with carbon dioxide supply also acts as a forced heat input and, therefore, iscomparable toheat from CUP.Hence, thereject heat of carbon dioxidesupplywasbrought intotheheating system atthesameplaceasthereject heat from CHP.  6.2.2 Detailed comparisons Tohaveahigh resolution comparison, adetailed study oftheperformance ofthe simulationmodelwasperformed takingaperiod ofonlythreedays.Thusthesample interval for the comparisons can be as small as 10minutes. However, some quantities, such as heating power and C0 2 supply appeared to be fluctuating in such awaythat boththemeasured and simulated values hadtobe filtered first to make them suitable for interpretation. The comparisons are made with respect to temperatures, humidity, C0 2 concentration of the greenhouse air, the heating power and controller actions (window aperture, thermal screens, artificial illumination and C0 2 supply). The three daysperiod under consideration used to provide the measurements for the comparisons started on 7January 1995.This period was selected because it consisted ofasequentialperiodwithlargevariationsofweather types.Thecourse of the outside air temperature in the selected period is shown in Figure 6.3.  108  Comparisons between simulation modelandmeasurements  Outsideairtemperature[°C]  6  12 18 07-01-95  6  12 18 08-01-95  6  12 18 09-01-95  Figure 6.3 Outside air temperature. Figure 6.3 shows that for about half the period, the outside air temperature remained below freezing point. On9January, thetemperature becomes quitehigh. The temperature drop during the morning of the seventh was caused by the fact that acloudednightwas followed byabright day.Figure 6.4,wherethe intensity ofglobalradiation isshown,confirms thebright day.Figure 6.5,showingthesky temperature, very clearly supports the assumption of a clouded night. The sharp decreaseofskytemperatures on7January,startingsomehoursbefore sunrise,can only becaused byaclearing sky.Atabout 16:00hoursofthefirstdaycloudiness again increases. The rest of the measuring period consisted of dull days, except for some clearing up on the third day. Globalsolarradiation [Wm!]  6 ^ ' 12 ' 18 09-01-95  Figure 6.4 Global solar radiation. 109  Results  Skytemperature[°C]  6  12 18 07-01-95  6  12 18 08-01-95  6  12 18 09-01-95  Figure6.5Sky temperature. Thecourse ofwind speed isshown inFigure 6.6. Onthe first day there ishardly any wind, but it speeds up on the other days, especially on 9 January. Windspeed [ms']  6  12 18 07-01-95  Figure6.6Windspeed Theoutsidevapourpressure isnotshownbecausethisquantityonlyplaysaminor role in the period under consideration (see the discussion on the comparison of measured and simulated window aperture, page 115). Thecomparison ofthemeasured andsimulated greenhouse airtemperature ofthe greenhouse compartment exposed totheoutsideweather conditions asmentioned above yielded the results shown in Fig. 6.7 till Fig. 6.15. Figure 6.7showsthatmostofthetimethemeasured andsimulated greenhouseair 110  Comparisons between simulation modeland measurements temperature agreeprettywell.Except fortheearlymorning ofthesecondday,the difference between measurement and model does not exceed 0.5 °C. Also the dynamics of simulated and measured data agree quitewell. The fast fluctuations of the simulated temperature between 4:00 and 8:00 on the second day originate from screen position variations during that time interval (see Figure 6.14). In reality the screen position was constant during that period and therefore the measured temperature did not show these variations. Airtemperature[°C]  '6  12 18 07-01-9S  6  Figure6.7Air temperaturesetpoint (air temperature.  l'2' 18 08-01-95  IT  12 l'£ 09-01-95  -) andmeasured(---)andsimulated (—)  The simulated and registered setpoint for the air temperature coincided, because thealgorithm applied intheresearch facility todetermine thesetpoint wascopied into the climate controller of the model. Note that on the first day the daytime setpoint (19 °C) is incremented with about 0.7 °C, due to the light dependent temperature setpoint increment. Observing Figure 6.7 it is striking that both the simulated and measured greenhouse air temperature significantly exceeds the setpoint for large sections of the period,althoughtheoutsidetemperatures aremuchlowerthantherequested inside temperature. Thismustbeattributed totheapplication ofaminimum pipetemperature. This minimum pipe temperature can be clearly seen in Fig. 6.8a and b, wherestrikingly constanttemperatures canbenoticed,especiallyduringthenight. The minimum pipetemperature for the daytime can be noticed only in the morning of the third day. On the first day this minimum pipe temperature has been lowered due to the high level of global radiation and on the second day thepipe temperatures are too high to be able to see the effect of the lower bound. Thecomparison ofthemeasured andsimulated supplysidetemperature ofthelowerheating circuit showsa goodsimilarity. However, thesimulated temperature 111  Results maxima oftheupperheating circuit aresmaller thanthemeasured values,butthe dynamics are still comparable. Temperature [°C] to 65 -_ ;S ij A  45-^  f J  it '/   ^  Al tJN   35- --••-'  \ t ll  V ' ' V  "f  —-»-|jy^-»v if - »,i  v. V  "  25 -_ 6  12 l'8 07-01-95  6  l'2" " 18 " " 08-01-95  6'  l'2 ' ' "l'£i " " ; 09-01-95 •  Figure 6.8aMeasured (-- -) and simulated(—) temperaturesjust behindthe mixingvalveof thelowerheatingcircuit. Temperature[°C]  6  12 18 07-01-95  6  12 18 08-01-95  6  12 18 09-01-95  Figure 6.8bMeasured (-- -) and simulated(—j temperaturesjust behindthe mixingvalveof the upperheating circuit. Contrary to the custom that only the primary heating system is bounded by a minimum pipe temperature, in the period under consideration the upper heating circuit was alsobound to a minimal value.This explains why even the temperature ofthesecondary heatingcircuitwasnot lowered duringtheperiodswhenthe air temperature exceeded the setpoint. Obviously, expressed in the lower temperatures simulated for the upper heating 112  Comparisons between simulationmodelandmeasurements circuit, the model underestimates the heat demand for some periods during the daytime of the second and third day. Figure 6.9, where the heating power is depicted, shows this more clearly. Heatingpower[Wm2] 200  6  12 18 07-01-95  Heat demand [MJ]  07-01-95  08-01-95  09-01-95  Figure 6.9Measured(-- -) andsimulated(—) heatingpower demand(a)and totaldailyheatdemand(b). Thecurves in (a)weresmoothedbya 6cell movingaveragefilter. The differences in computed and measured heat consumption on the second and third dayarealmost 10%.Oneoftheexplanations for these differences isthe fact that the real climate controller induces more overshoots than the simulated one, as can be seen in Figure 6.7. In Figure 6.10 can be seen that the vapour pressure deficit was described very well.  113  Results  Vapour pressure deficit [gkg'1]  4-  A*  J r  3_ 2-  .' ' 6 " 1'2 1'8" " 07-01-95  6  1'2 1'8 08-01-95  6  1'2""1'8"" 09-01-95  Figure6.10Measured(-- -) andsimulated(—) vapourpressure deficit. Combining Figure 6.7 and 6.10 with Figure 6.11,which showstheWindowaperture, demonstrates the importance of the simulation of humidity. The humidity controlleropensthewindowsproportional totheviolationofthehumidity setpoint whichwas3gkg"1duringthenight and3.5gkg'1duringtheday.The combination ofthe figures showsthatthe window aperture during daytime of thethird day is governed by the humidity controller, rather than by temperature control.  Windowaperture [%] 108-  > ''AMft  64-  1 '"  2-  i  :  6  12 18 07-01-95  6  12 18 08-01-95  /  6  kA  12 18 09-01-95  Figure6.11 Registered(- - -)andsimulated(—) windowapertures.The curves in(a)weresmoothedbya 6-cell movingaveragefilter. In Figure 6.11, it is significant that the windows are not opened during thefirst part of the period under consideration. This has to do with the prevention of 114  Comparisons betweensimulationmodelandmeasurements window control during a period of frost in order to eliminate the risk of severe damage dueto opening awindow frozen fast by ice. The fact that duringtheeveningofthethird day simulated windowswere opened to a smaller extent than the measured aperture is aresult of the lower humidity computed by the simulation model for that time. The third important entity of the greenhouse air is the C0 2 concentration. In Figure 6.12 the computed values are shown together with the measured values. The controller maintains the C0 2 concentration at 900 ppm during daytime and duringthenightwhentheartificial illumination isswitchedon.Unfortunately, the decay oftheC0 2 concentration intheresearch facility canhardlybeseenbecause for most of the nighttime without illumination the measuring device is switched off. It is switched off to prevent the device sucking in sulphur, which is evaporated in the greenhouse air during the first hours of the night to avoid diseases (erysiphaceae).However, the first part of the decay-curves after the C0 2 supply isstoppedandtheresponseoftheC0 2 concentration onthere-start ofC0 2 supply is very similar.  1000  COjconcentration [ppm]  6  12 18 07-01-95  6  12 18 08-01-95  6  12 18 09-01-95  Figure 6.12Measured(-- -) andsimulated(—) C02concentration. In the research facility the C0 2 supply isperformed by a valve that controls the addition of pure C0 2 . The valve is either activated or closed. If activated, the valvepasses 1.9-10'6kgC0 2 m ' V . The mean supply rateresultingfromthisonoff control isdepicted inFigure 6.13.The data of the curve havebeen smoothed by a 20 cells moving averagefilter. Thedynamics of thesimulated and registered supply rate arevery similar buton the second day the total amount of C0 2 supplied in the simulation model issignificantly higher. An explanation for the fact that the matching is quite good on the first and last day and worse on the second day is probably the existence ofa 115  Results strongC0 2 gradient inthecanopyregion.Becausethecanopywasplantedonmovable benches andthe C0 2 measuring device sucked itsair samples from a fixed location, it is conceivable that the samples were taken from aregion with arelatively high C0 2 concentration on one day and from a region with a different regime on another.  C0 2 supply rate [mgm 2 s 2 ]  12 18 07-01-95  6  12 18 08-01-95  12 18 09-01-95  Figure 6.13 Registered(-- -) andsimulated(—•) C02 supplyrate. Finally, Figure 6.14 showsthestatus ofthethermal screen andFigure 6.15show the status of the artificial illumination. In both model and reality the thermal screen is hardly ever closed completely on these three days. The crack in the screen is to carry off moisture when the vapour pressure deficit is lower than 3 gkg'1 (the nighttime humidity setpoint). This can be seen very clearly in the simulation results where in the early morning of the second day the vapour pressure deficit iskept constant at 3gkg"1 by a constantly changing screen position. Only in the early morning of 7 and 8January is the humidity criterion satisfied (which is3.5 gkg"1for thedaytime, includingtwohoursbefore sunrise).Thenthe screen is fully closed for a small time. As can be seen in Figure 6.3 the outside temperature remained higher than 5 °C during the evening of the last day.This prevented the screen from being closed.  116  Comparisons between simulation modelandmeasurements  Screen position [%]  6  12 18 07-01-95  12 18 08-01-95  6  12 18 09-01-95  Figure 6.14Registered(-- -)andsimulated(—) screenposition.  Artificial illumination  6  12 18 07-01-95  12 18 08-01-95  6  12 IE 09-01-95  Figure6.15Registered(- - -)andsimulated(—) statusofartificial illumination The artificial illumination can be expected to follow the registered status almost exactly, because its status is controlled by the same algorithm as applied in the research facility. The only case where deviations may occur is during daytime when the intensity of solar radiation fluctuates around the intensity at which the lights are switched on and off. This occurs once on the second day.  117  Results 6.2.4 Comparisons for a year round period The experimental data that serve as a reference for the long-time comparisons were gathered for thetime span of ayear. This year started on 1 February 1993. Tolimittheamount ofgraphs,theshowedcomparisons arerestricted totemperature, heat demand and water consumption. Figure 6.16 shows the measured and simulated daily mean greenhouse air temperature. Temperature [°C]  mar ' apr Figure 6.16Measured (- - -) and simulated (—) daily mean greenhouse air temperature. The daily values were smoothed by a 4 cell moving averagefilter. In general the simulated temperature isquite similar tothemeasured values, but during warm periods the model tends to compute higher temperatures. Since in thoseperiods the windows are fully opened, it is likely that theventilation capacity ofthe real greenhouse at maximal window aperture ismore than the air exchange rate resulting from De Jong (1990) (see Section 5.5.2.1). In Figure 6.17 the measured and simulated daily heat demand of the greenhouse aredepicted.Theagreement between model andmeasurement isgood.Onlyduring the quite extreme cold period at the end of November does the model show an important lower heat demand. Thetotal heat demand computed bythe model, 1743 MJm"2, is a bit lower than the measured total, which was 1782MJm'2 (a difference of2%). InFigure 6.17, itis interestingtoseethatduring summer theheatdemand isstill about a quarter of the heat demand in winter, whereas the mean difference betweentherequested greenhouse airtemperature andtheoutside air temperature is far much smaller in summer than in winter (see Fig. 6.18). This high heat demand in summer must be attributed to the minimum pipe temperature, which was40 °C during theday (but diminished on global radiation) and 45 °C during the night. 118  Comparisons between simulation modelandmeasurements  1  feb ' mar ' apr ' may' jun ' Jul ' aug ' sep ' oct ' nov ' dec ' jan '  Figure 6.17 Measured(-- -) and simulated (—) dailymeanheatdemand. The dailyvalueswere smoothed. 30-  Temperature[°C] temperaturesetpoint.  -10-  •feb ' mar ' apr ' may' jun ' jul ' aug ' sep ' oct ' nov ' dec ' jan '  Figure 6.18Outside dailymeanair temperature anddailymeangreenhouse air temperature setpoint. The third measured quantity that iscompared tothe simulated values isthe daily water consumption. Obviously themodeltendstocompute ahigher daily evaporation than registered. Themostimportant differences occurinMarch,thesecondhalfofAprilandMay. A possible explanation for these differences is the fact that the response of stomatalresistance toenvironmental factors suchastemperature andvapourpressure deficit ofthe greenhouse climate isnotconstant duringtheyear. From horticultural practice it is well known that at the end of winter, roses have very thin leaveswithalimited evaporation capacity.Inthepresent work itwasnotpossible to quantify this effect and thus the coefficients applied todetermine the stomatal resistance remain constant throughout the year. This resulted in a serious over estimation of the evaporation at the end of winter and spring. 119  Results  Water consumption [kgnv'day1]  C  C.  CO  O  0 B  l A A A / lA A /' V  2.5^ 2.CH 1.5-^ 1.0-E  "^CTTW  CO c  1111111  o c  ' feb ' mar ' apr ' may' jun ' Jul ' aug ' sep ' oct ' nov ' dec ' jail ' Figure 6.19Measured(-- -) andsimulateddaily water consumption  6.2.4 Conclusions on the model evaluation Theresemblancebetweenthemeasurements andmodelcomputations isgood. On a small-time scale the dynamics of the modelled quantities are very much the same as the measured values, although sometimes distinct differences can be noticed, especially as far as carbon dioxide supply is concerned. The greenhouse climate controller actions of the model were in line with the actions of the controller of the research facility that served as a reference. On ayear roundtime scale,thetemperatures and heat demand ofthe greenhouse arewelldescribed bythemodel.The computed yearly heat demand wasonly2% lessthanthemeasured heat demand. Moreover, the deviation between computed and measured heat demand was concentrated in a short period of extreme cold weather. The simulated daily mean greenhouse air temperature deviated only duringverywarmperiodsfrom themeasuredvalues.Thenthesimulated temperature ishigherthanthemeasured value.Thiswasattributed toanunder-estimation of the ventilation capacity. The daily water consumption was over-estimated by the model.  120  Evaluationof energy saving techniques 6.3 EVALUATION OF ENERGY SAVING TECHNIQUES  In Chapter 2 three groups of energy saving measures were formulated to be studied. Inthepresent sectionthese measures are determined bymeansof theapplication of the simulation model developed. In all computations the growth of a tomato canopy intheNetherlands ina modern greenhouse of 1hectare serves as a horticultural reference. In Section 6.3.1 the requested greenhouse climate with respect to the growth of tomato is outlined briefly. The parametrization of the large greenhouse isvery much alikethe construction oftheresearch facility discussed in Section 6.2.1. However, in Section 6.3.2 some typical scale affected variablesarere-parametrized tosuitacommercial greenhouse.InSection6.3.3the weather conditionstowhichthegreenhouse inthesimulations isexposed arepresented. In Section6.3.4 thethreeclusters ofenergy savingoptionswhichwerementioned in Chapter 2 are evaluated.  6.3.1 Requested greenhouse climate conditions for the growing of a tomato crop The growth of crops in modern protected cultivation isahighly professionalised activity. Skilful and well-educated people continuously adapt the greenhouse controller settingsinordertocreate afavourable environment for canopy growth. Obviously,these continuous adaptationsresult inavagary course ofclimate controller setpoints. However, in order to simplify the definition of the requested greenhouse climate conditions for the greenhousethatservesasareference inthe major part of this chapter, a broad outline of the course of climate controller setpoints is applied. The reference greenhouse starts its growth season in December when the young tomatoplants areplanted.Duringthefirst threeweeksthedaytime andnighttime temperature setpoint are 18 °C. The light dependent temperature setpoint increment is2°Cfor outsidesolarradiation intherange from 50to250Wm*2.During the first months of the growth, no minimum pipe temperature is applied. The maximum carbon dioxideconcentration issetto700ppm.Carbon dioxide issupplied by exhaust gases from the combustion of natural gas at arate of 40m3 gas perhectare per hour. Heatsurpluses from C0 2 supply are stored inaheat storage tank. When the storage tank is completely charged the combustion for carbon dioxide supply is stopped. The humidity setpoint issetto 85%RH.If theactual humidity inthe greenhouse exceeds the setpoint thewindows are opened proportional tothe excess with2% window opening per percent excess of the RH. Thesecondary heatingcircuit accompaniestheprimary circuitwhenthetempera121  Results ture ofthe latter exceeds 55°C.The windows are opened when the air temperature exceeds the setpoint by 0.5 °C. The opening angle is proportional to the excess, with a proportional band with a minimum of 4 and increases linearly to 8ontemperature difference betweenairtemperature setpointandoutsidetemperature. The maximal proportional band is reached when the outside temperature is 8 °C below the air temperature setpoint. After thefirstperiod ofthreeweeksthedaytimetemperature setpoint isincreased to 19 °C and the nighttime temperature setpoint is lowered to 17 °C. All other settings are left unaltered. OnthefirstofAprilthedaytime andnighttimeminimum pipetemperature areset at45 °Cand40°Crespectively. During daytime,theminimum pipe temperature isloweredlinearlytowardstheairtemperature setpointforoutsideglobalradiation in the range between 100 and 300 Wm"2.All other settings are left unaltered. On 1September the humidity setpoint is lowered to 80%RH. The growth season endson 11 November. Onthat daythenighttime air temperature and all minimum pipe temperature setpoints are lowered to 5°C. Humidity control andcarbon dioxide supplyareabandoned. Toprovide acomfortable temperature during daytime, when a lot of work is being carried out in the greenhouse, the daytime temperature setpoint is set to 15°C. On 26November the air temperature setpoints are increased to 18°C.  6.3.2 Geometry of a large commercial greenhouse TheVenlo-typegreenhouse,which iscommonly appliedintheNetherlandsisbuilt from arepeatedsequenceof3.20mwideroofsegments.The 1 hectaregreenhouse subject in this study is composed of 30 of these roof segments, and thus, the lengthofthegreenhouse is 104meter. The floor togutterheight isassumed tobe 3.5 meter. Therefore, the sidewall/surface ratio of the greenhouse is 0.15. The gutter orientation is north-south. One window per eight glass panels is mounted in each side of the greenhouse cover.The glasspanels are one meter wide.Thus thenumber ofventilating windowsperm2greenhousesurface equals 1:12.8=0.078.Thewindowsaretwoglass panels wide and halftheridge-gutter distance long.The roof slope is25°.Hence the area of one window equals 1.8 m2. When the windows are closed the leakage of the greenhouse is assumed to be 1.25-10"4m3per m2greenhouse per unitwind speed (ms'1). This figure isamean of the leakages determined by De Jong (1990) in four commercial greenhouses. The greenhouse has a lower heating circuit with four pipesper roof segment and an upper heating circuit with half as many pipes.The capacity of the circulation pumps inthe upper and lower heating circuits are 30m3 per hour and 90m3per  122  Evaluationof energysaving techniques hour respectively. The diameter of the lower heating pipes is 51mm. The upper heatingpipeshaveadiameter of28mm. The upperheatingcircuit servesboth as a secondary heating circuit and as a heat dispenser for the condenser. If the heatingsystemcomprisesacombinedheatandpowerengine(seeSection6.3.4.3), the condenser isused by both the boiler and the CHP engine. Thegreenhouseboilerhasaheatingcapacity of2.5MW.Theconversion efficiency of the boiler is 0.85 with respect to the upper heating value of natural gas, which isacustomary value for modern boilers (Handboek VerwarmingGlastuinbouw, 1995). Heat surpluses are temporary stored in a storage tank of 80m3.  6.3.3 Weather data Outside weather conditions have a considerable impact on the course of heat demand of a greenhouse.Therefore, in order tojudge thepossible energy-saving options for situations intheNetherlands, thesimulation model hastobe fed with typicalweather data for theNetherlands.The definition of suchatypical weather cannot be based on mean levels of meteorological quantities, but also has to includetheirdynamics.Such asetofweather data for theNetherlands canbe found inthe SEL-year (Breuer &Van deBraak, 1989).The SEL-year isacomposition oftwelvesetsofrealmonthly weather data.Each setofmonthly dataintheSELyear has been selected from 17 sets of real weather data for that month. The 17 setswere gathered between 1970and 1986inDeBiltbytheRoyal DutchMeteorological Institute.Theselectionwasmadeinsuchawaythatthetemperature and radiation data are in fair agreement with mean weather characteristics for the month under consideration intheNetherlands. This meansthat, for example, the weather data measured in January 1971, serve as typical weather for January, whereas the SEL weather data for February were measured in 1973. Thedatafilecontainsrecords ofhourly weather datathatconsistsoftemperature, radiation and humidity. The SEL-year does not provide information on the sky temperature. Because the model requires this virtual temperature, the algorithm presented inappendixFhasbeenused(Eqn.F.6).Thefraction oftheskycovered with cloudswas estimated comparing diffuse and direct radiation withthemaximal intensity of global radiation for each hour in the datafile. Also the data on rain fall, present in the SEL-year have been applied to estimate the cloudiness. Finally, the slope of the course of nighttime temperatures were applied to getan indication of cloudiness. InFigure 6.20 themean monthly temperatures andmonthly radiation totalsofthe SEL-year are compared to the same quantities between 1990 and 1994.  123  Results  The pictures show a large variation of monthly values, but indeed the SEL-year appears to represent the weather data in a reasonable way. (a) Outside temperature [°C] 4J  20to  *-o >s$ yr^M> V*J>  ^ s  O  wi/M  •<  SEL  MA  CO c  ......L  - __- - .  ....:..  jan feb mar apr may jun Jul aug sep oct nov dec  (b) Global radiation [MJnr'dag l ]  jan feb mar apr may jun  aug sep oct nov dec  Figure 6.20 Mean monthly temperatures (a) and monthly totals of global radiation (b) in the SEL-year data set compared to measurements in De Bilt between 1990 and 1994  124  Evaluationof energysaving techniques 6.3.4 Energy saving prospectives In thedocument on the MJA a large number of energy saving measures aresuggested inorder todecrease theenergy consumption of glasshouse horticulture. In this section, the prospectives of six of the proposed measures will be evaluated. InChapter2,theproposed measureswerearranged inthreeclusters.Thefirstitem concerns relatively simple improvements to the heating system. With respect to this itemtheeffect oftheinsulationthicknessoftheboiler, insulation oftransport pipesandtheconnection oftheexpansionvesseloftheheatingsystemarestudied. Theseconditemconcernsimprovements tothegreenhousebuilding.Theheatloss from the building can be decreased by eliminating cracks in the cover, by the application of thermal screens and by the application of alternative cladding materials. Thethird iteminvolvestheapplication ofenergy-saving heatingdevices.Herethe energysavingeffects ofacondenser, ashort-term heatstorage facility andacombined heat and power engine will be studied.  6.3.4.1 Simple improvements of the heating system Thefirstrequirement for anefficient application ofheat istoprevent heatrelease in places where there isno need for heating. This can be achieved by insulating theboiler andtransport pipes.Alsotheconnection oftheexpansion vessel affects the extent of unnecessary heat loss. In the following the simulation model (or a part of it) is applied to compute a theoreticalvaluefor theenergy savingsthatcanbeexpectedfromthesemeasures.  Insulation ofthe boiler Contrary to all other options discussed in this section, the complete greenhouse climate simulation model isnotrequired to compute the energy savings from the insulation oftheboiler. This isbecause, inorder toavoid condensation insidethe boiler, thetemperature ofthewater inaboiler iskept ataconstant levelof90°C throughout the year. Thus the boiler sub-model, presented in Section 4.4.3, suffices. Inthesub-model theheatlossfrom theboilersurface isafunction ofthetemperature difference between the water inside the boiler and the temperature of the environment and insulation thickness. In Figure 4.11 the relation between the overall heat exchange coefficient and the insulation thickness was shown. Multiplication of the heat exchange coefficient with the surface of the boiler and the appropriate temperature difference yields a heat loss. Multiplying the heat loss  125  Results with the time span of a year gives the yearly energy loss. To show the effect of insulation thickness, aboiler insulated with 2 cm of rockwool was compared to a boiler insulated with 6 cm of rockwool. Assuming the mean(air andradiation) temperature oftheenvironment oftheboilertobe20°C, theresults for aboiler with adiameter of 2.3m and a length of 4.6 m are stated in Table 6.1.The assumed dimensions are typical for a boiler of 2.5 MW. Becauseinhorticultural practiceenergysavingsaremostlyexpressed inm3natural gas, theenergy savings areexpressed inboth m3ofnatural gas inGJ.To convert thesavingsfrom GJtom3aconversion efficiency of0.9withrespecttotheupper heating value was used. Table6.1 Yearlyenergylossof a boilerat 90 °Cwith a lengthof 4.6 m anda diameterof2.3m toanenvironment at20 °Cfor an insulation thickness of 2 cm rockwool and 6cm rockwool. insulation thickness  energy loss of energy loss of front the side wall and rear side GJyear'1  GJyear"1  total energy loss GJyear'1  m3year''  2cm  105  24  129  4316  6cm  42  n  53  1773  From the table it can beseen that aboiler insulated with only 2 cm of rockwool has a yearly energy loss of 129 GJ. An increment of the insulation up to 6 cm decreases the yearly energy loss to 53 GJ. Comparinglossescomputedbyapplicationoftheboilermodelwithempiricaldata as presented byNawrocki &van der Velden (1991) the latter appear tobemuch larger. In their work the weekly energy loss contributed to the boiler wasfitted into an empirical formula reading: L = -182 + 1 2 7 2 ^ ^  (6.1) [m3 week'1]  insu  whereListheweeklyenergy lossinm3ofnatural gas,C ^ ^ themaximal heating capacity of theboiler in MWanddinsuthe insulation thickness ofthe sidewall in cm.Multiplication ofthe figures inEqn.6.1with a factor 1.65 turnsthe equation into arelation that expresses the yearly energy loss in GJ per year. Application oftheempirical formula tocomputetheeffect oftheincrement ofthe insulation thickness from 2to6cm results in anenergy saving effect of 1749GJ per year. Thus, the empirical formula gives an energy saving that is 23 times larger than the theoretical approach. The major part for the large difference between the result of Eqn. 6.1 and the theoretical value must be attributed tothepeculiarity that heat lossesthat arenot expected to bedependent on insulation thickness (losses from valves,pumps,the 126  Evaluationof energy saving techniques feet of theboiler, thefrontandrear side), are somehow included intheterm that describesthedependencyoftheenergy lossoninsulationthickness.What'smore, the constant, from which itwould be expected that ittakes account of insulation independent losses, is negative. Observingthedifference between thetheoretic computations andthepeculiarities oftheempirical relation posed byNawrocki &Van der Velden, additionalmeasurements accompaniedbyamoredetailedmodelontheheatlossesfrom theboiler should becarried outto giveaplausible relation tocompute theenergy lossfrom a boiler.  Insulation of transport pipes  Theheat release oftransport pipes ina greenhouse canplay apositive or anegativeroleintherealizationofauniform temperature distribution inthegreenhouse. Generally speaking, the heat release is included in the design to compensate for heat lossesnear walls,buttransport pipes can alsodisturb thetemperature distribution. In the latter case, insulation of thetransport pipeshas apositive effect on the homogeneity of the greenhouse air temperatures and saves energy aswell. To compute the energy saving, it issufficient to know thefrequencydistribution ofthetemperature excessofthetransport pipes relativetotheir environment and the heat loss of pipes as a function of insulation and temperature excess. In this section, first thefrequencydistribution curves are presented. Then the heat loss ofpipeswith andwithout insulation as a function oftemperature excess isdetermined.Finally,theenergy-saving effect of insulatingthepipetypesdistinguished is computed. The energy-saving achieved by insulation iscomputed for six types of transport pipes,namely themain supply and gathering pipe (see Fig.4.3) and thetransport sections of the supply andreturn sidesof both the heating circuits (see Fig.4.4). The frequency distribution of the temperature excesses of these six pipe types weredetermined bythesimulation model.Theresults arepresented inFigure6.21 and 6.22. Figure 6.21 shows that the main supply pipe is at 90 °C for most of the time. Only during discharge ofthe heat storage tank does itstemperature decreases to thesetpoint ofthe lower heating circuit. Thetemperature ofthe gathering pipe is a weighed mean temperature of the water returning from the upper and lower heating circuits. Comparison of the dashed curve in Fig. 6.21 and the dashed curves inFig. 6.22 showsthatthereturn temperature ofthe lower heating circuit dominates the temperature of the water in the gathering pipe. This is not surprising since the upper heating circuit withdraws water from the main supply pipe only during periods with a high heat demand. Moreover, the maximal 127  Results  contribution of the upper heating circuit to the flow through the gathering pipe is only lA. Hours 12001000^  main supply pipe  1S  800-^    600^  gathering pipe '.  '* /  400^  i s / i <  /  ' 'x  '  1  /  /  200-^  o-  -  —  .  0  —  i  10  —  .  —  i  20  •  i  i  30  i  —  i  40  **i •  • i  50  i  i  —  .  i  —  i  —  •  60 70 80 temperature excess PC]  Figure 6.21 Frequency distribution of pipe temperature excess relative to the greenhouse air of the main supply pipe and the gathering pipe. Hours lower heating system -supply side return side lower heating system „ return side supply side  50 60 70 80 temperature excess PC] Figure 6.22 Frequency distribution of pipe temperature excess relative to the greenhouse air of the supply and return side of the heating circuits. Figure 6.22 shows that the upper heating circuit has rather small temperature excesses most of the time. This is due to the fact that most of the time the pipe temperatures of the upper heating circuit are a result of heat produced by the condenser. The majority of the time, the upper heating circuit is about 7°C higher than the air temperature. During this time the heat produced by the condenser ori128  Evaluationof energysaving techniques ginates intheboiler that combusts gas for thecarbon dioxide supply. Thesecond peak in the frequency distribution curve of the upper heating circuit (around an excessof 14°C)istheresult oftheminimum pipetemperature inthe lowerheating circuit. Theeffect oftheminimum pipetemperature onthetemperature inthelowerheating circuit can be seen in the first peak of the supply side temperature excess of thisheating circuit, located around atemperature excess of 23°C.This temperature excess is caused by a minimum pipe at 40 °C and an air temperature at-17 °C.Thesearethenighttimecontroller settingsbetweenApril andNovember.Near to the first peak, a second, somewhat lower peak, at a temperature excess of 25 °C can be observed. This peak must be attributed to the daytime minimum pipe temperature of 45 °C, accompanied by an airtemperature of 20 °C. This peak is lowerthanthefirst,becauseduringdaytimetheminimum pipetemperature isdecreased on outside global radiation (see the climate controller definition onpage 122)andtheairtemperature often exceeds20°C.Thedashedreturn temperatures follow the supply temperatures with atemperature difference (due totheheatrelease inthedistribution loops) that increases asthetemperature excess increases. Ona onehectare greenhouse, the supply and return pipes of theupper and lower heating circuits are commonly made from piping material with a diameter of90 mm and 180 mm respectively. The diameter of the main supply and gathering pipe isalso 180mm.The convectiveheatexchangecoefficient ofthesepipeswas computedusingthetheorypresented inappendixAasafunction ofpipetemperature. The air temperature was assumed to be 20 °C. The radiative heat loss of thesepipeswascomputed byassuminganemission coefficient of0.84andanoptically black environment at 20 °C. In Figure 6.23,the total heat loss, being the sum ofbothheatexchangemechanisms, isexpressed per meterpipe asa function of temperature excess for both pipe diameters. The heat loss per meter pipe as a function of the temperature excess of the 180 and90mmpipesafter insulationwith3cmrockwoolcovered byaluminumplates is shown in Figure 6.24. The thermal conductivity of rockwool was set to 0.04 Wm"'K'' (Polytechnisch zakboekje, 1987)andtheemission coefficient ofthealuminum covering was set to 0.3 (Handbook of Chemistry and Physics, 1968). Comparing they-axes of Figures 6.23 and 6.24 shows a decrease of heat release with a factor of around 10. The energy savingthat results from the insulation of thepipescan nowbedetermined bythesum ofthemultiplication ofthesavings achieved for eachtemperature excess with the yearly duration of that temperature excess for a particular type of pipe. InTable6.2theresults ofthiscomputation for thesixtypesoftransport pipesare stated. 129  Results Heat loss [Wm1] 500-  180mm diameter 400-  300-  200  100-  40  50 60 70 temperature excess [°C]  Figure 6.23 Heat lossper meter pipe for twopipe diameters as afunction of temperature excess. Heat loss [Wm1] 50  180mm, insulated 40-  30  20-  10  50 60 70 temperature excess[°C] Figure 6.24 Heat lossper meter pipe of a 90 mm and 180 mmpipe isolated with 3 cm rockwool and wrapped with aluminium plates to an environment at 20 °C as afunction of water temperature excess inside the pipe.  130  Evaluation of energy saving techniques  Table 6.2Decrement of theyearly energy lossper meterpipe due to insulation for six types of transport pipes. The transport pipes of the upper heating circuit have a diameter of 90 mm. The other pipes have a diameter of 180 mm. Insulation wasperformed with 3 cm rockwool, covered with aluminum plates. type of transport pipe  energy loss of uninsulated pipe GJm"'year"1  energy loss after insulation  15.28  1.45 0.50 0.54 0.29 0.25 0.14  main supply pipe gathering pipe low. heating circ. supply return upp. heating circ. supply return  4.44 5.01 2.58 2.09 1.06  GJnr'year'1  energy saving per meter pipe due to insulation m'nr'year"1 GJnr'year'1 13.84  437  3.93 4.47 2.28 1.84  214 141  0.93  72 58 29  The results of Table 6.2 can be applied to answer the question whether or not it is economically attractive to insulate transport pipes at places where the heat release is not wanted or not necessary.  Connection of the expansion vessel If an expansion vessel is connected to apart of the heating system with predominantly high temperatures, a relatively simple measure to conserve energy is to change the connection of the expansion system to a part of the heating system with low temperatures (van der Velden et.al, 1993). Heat losses from the expansion system emanate from the inflow of water into the expansion vessel (when the mean temperature of the water in the heating system increases) which is returned at a lower temperature (when the mean temperature of the heating system drops). Insulation of the vessel in order to decrease its heat loss is discouraged by installers because it has been experienced that current expansion vessels do not withstand a continuously high temperature. The computation of the amount of energy conserved by changing the place of attachment of the expansion system cannot be computed with frequency distribution curves like Fig. 6.21 and 6.22, because the inflow and residence time of the water in the vessel also have to be known. Instead, the heat losses from the expansion vessel were computed by the simulation model which was evaluated once with the vessel connected to the hottest part in the heating system (the pipe segment that transports the water from the boiler to the main supply pipe) and once with the vessel connected to the gathering pipe. The comparison of the heat losses of a relatively hot and a relatively cold expansion vessel are studied for two cases. The first case concentrates on the reference 131  Results greenhouse,withaheat storage tankof 80m3ha"'.For thisgreenhousetheexpansion vessel has to have a volume of 3 m3. In the second case the effect of the connection place ofthe expansion vessel of a greenhouse without a heat storage tank isstudied. Theexpansion vessel inthe second case ismuch smaller, namely 0.5 m3. The dimensions of the storage vessels were computed from the volume difference of the entire water content of the system at 90 °C and at 20 °C. The computed daily energy losses are plotted for both options in Figure 6.25. Daily energy loss [MJ] 140 120  reference greenhouse 'hot' vessel 'cold' vessel  100-  1  dec I jan ' feb ' mar ' apr ' may ' jun ' Jul ' aug ' sep • oct ' nov '  Figure6.25Dailyenergylossesofa 'cold' (dashedlines)anda 'hot'(full lines) connectedexpansionsystemfor the referencegreenhouse,andfor a greenhousewithoutaheatstorage tank. Ofcourse,theenergy lossesfrom thelargevolume expansionvessel ofthegreenhousewiththestoragetank are morethanthelosses from theexpansion vessel of theother greenhouse. Forthegreenhousewiththeheat storage tankthelossesare concentrated in the summer, because in that period the heat storage tank is used intensively.Anintensively used storagetank implies largevolume differences of thewaterinheatingsystem becauseamassive amount ofwaterinthestoragetank is heated and cools down every 24 hours. For the greenhouse without a storage tankthe energy losses inwinter are larger thanthe losses in summer because the temperature variations of the heating circuits are larger in winter. In Table 6.3 theyearly cumulated energy losses for both connection options are stated.Fromthetablecanbeconcludedthattheenergy savingachievedbychangingtheconnection oftheexpansion vessel from thehottestpart tothecoldestpart is about 9 GJ for a greenhouse with a small vessel and increases up to 20 GJ when the greenhouse is equipped with aheat storage tank. However, the energy saving effect found with the simulation model is much smaller than the results 132  Evaluationofenergy saving techniques reported by Van der Velden &Nawrocki (1991). It could bededuced from their work that they estimated the yearly extra heat losses of a 'hot' expansion vessel compared to a 'cold' one at 270 GJ. This value was not related to the sizeof the heat storage facility, nor to the water content of the rest of the heating system. Table 6.3Yearlyenergylossfroma 'hot'and a 'cold'connectedexpansion vessel for thereferencegreenhouseandagreenhouse withoutaheatstorage tank.  reference greenhouse (storage tank of 80 m3) greenhouse without a storage tank  'hot' expansion vessel GJyear"'  'cold' expansion vessel GJyear"'  29.2  8.9  20.3  642  12.8  3.8  9.0  284  energy saving by changing the attachment GJyear'1 m'year"'  Theempirical valueismuch larger than the differences computed bythe simulation model. However, the value presented by Van der Velden and Nawrocki is rather unlikely, since a heat loss of 270 GJ requires that the mean expansion vessel temperature is about 80 °C hotter than the 'cold' vessel, throughout the year. This figure was computed assuming an expansion vessel with avolume of 3m3(enough for agreenhouse ofonehectare with a80m3storage tank),anoutside surface of 11 m2 (about the size of the one depicted in Fig. 4.21) and an overall heat exchange coefficient of 12Wm"2K'' (which is quite high). Havingnoticedthe large discrepancy between theresultsofthesimulation model and theempirical data and the questionable results presented by Van der Velden &Nawrocki,additional measurements should becarried outpriortothedevelopment of a more detailed simulation model.  Conclusions Amongthesimpleimprovements totheheatingsystem,theinsulationoftheboiler andthe insulation oftransport pipes arethemeasures thatare most likelytoyield thehighest energy savings.However, because changingtheattachment oftheexpansionvesselisquiteeasy,thepriority sequenceofmeasurestosaveenergyfrom simple improvements will probably start with the connection of the expansion vessel.  133  Results 6.3.4.2 Improvement of thebuilding The transmission of solar radiation by the greenhouse cover is of utmost importance for a high productive horticulture. Therefore, at present, greenhouses are covered with glass.However, thethin glasspanes(4mm) havea lowthermal resistanceandahighemission coefficient for long-waveradiation.Consequentlythe heat lossesthrough the covering structure are large.Also,inorder tohave ahigh transparency, the mechanism to control the aperture of ventilating windows is madeassmallaspossible.However,thisdelicatemechanism isvulnerable.Therefore, there is quite a risk that when the mechanism is not periodically adjusted, some windows can no longer be closed completely. In thissection the energy savingeffects of adjusting the window aperture control mechanism and measures todecrease theheat lossesatthecover arestudied.The latter isachievedby anumber ofmeasures, includingtheapplication ofathermal screen and alternative cladding materials. Animportant disadvantageofathermal screen andofcurrent alternative cladding materials isthe decreased transparency of the covering structure. This leads toa decreased biomassproduction. Therefore, whenstudyingthedifference inenergy consumption which results from applying different energy saving measures that affect thetransparency ofthecover,theenergyconsumption mustbecorrected for possibleproductionlosses.Thus,withrespecttothesemeasures,theenergy-saving effect isexpressed interms ofspecific energy consumption (theenergy consumption per unit of production), instead of the energy consumption per m2. In the present model, the computation of production is limited to the first step of biomassproduction, beingthephotosynthesis.Therefore thespecific energy consumption is defined as the yearly primary energy consumption divided by the yearly sum of photosynthesis. The specific energy consumption is expressed as MJkg1. Another aspectoftheimproved insulationofthegreenhouse isitseffect onhumidity. In a customary, single glass cladded greenhouse, in winter, a large amount of moisture condenses at the cover. Thus,the greenhouse air is continuously dehumidified. Sometimes, this (uncontrolled) dehumidification results in an unfavourably dry indoor climate, butmore often condensation preventsthehumidity exceeding the setpoint. If the insulation of the greenhouse increases, which is accompanied by higher covertemperatures (alternative claddingmaterials) oranobstructed vapourtransporttothecover(athermal screen),condensation diminishes.Thus,windowshave to be opened more frequently to carry off moisture. So, part of the benefits of increased insulation are lost by the necessity of increased ventilation. Increased (controlled) ventilation isalsonecessary when theairtightness ofthe greenhouse is improved by better closing windows. To give an impression of the order of magnitude oftheamount of energy consumed asaresult ofventilation onbehalf 134  Evaluationof energysaving techniques of humidity control, in all tables of the following sections the portion of the energyconsumption associatedwithcontrolled dehumidification ispresented. For each case,theportion isdetermined by comparing theresultsoftwosimulations. For each second simulation all settings are equal to the first, except for the setpoint for the humidity controller, which is increased from 85% RHto 100%RH, resulting in the absence of humidity control.  Improved air tightness An important source of leakage in a greenhouse is the fact that sometimes windowscannotbeclosed.Inagreenhouse,alargenumberofventilators arecoupled toone mechanism that controls theaperture. Therefore, aslovenly tuneupofthe mechanism can easily mean that a number of ventilators cannot be closed completely.Togiveanimpression oftheenergy lossduetosuchashortcoming tothe ventilators the simulation model is applied once with perfectly closingwindows, and once for a case where 20%of the windows remain open with a slit of 1 cm (=0.72°, =2%). The results are presented in Table 6.4. The considered measure is not likely to affect production. Therefore the correction for effects on photosynthesis can be omitted. Consequently the energy consumption is expressed inGJm"2year"1. Table 6.4 Yearlyenergyconsumption andenergysavingofagreenhousewithwell closingwindows comparedtoagreenhouse withaslitoflcm in 20% of thewindowswhenthewindowsaremeantto be closed.  cracks reference  energy consumption GJm'2year"' 2.045 2.013  portion for dehum. MJm"2yeaf' % 2?6 U 219 U  energy saving MJm"2year"' % '"• 32 1.6  The computations show that the small cracks in 20% of the windows induce an increment of energy consumption of only 32 MJper m2per year (1.6%). Asexpected, the portion of the energy consumption for dehumidification decreases when the uncontrolled ventilation of the greenhouse grows, although in the considered case the effect is hardly noticeable.  135  Results Application of a thermal screen The effect ofanoverhead thermal screen onheatdemand depends onthecharacteristics of the screen and the horticultural environment in which the screen is applied. As far as this study is concerned, only the characteristics of an LS-10+ screen tissue were available, because this type of screen was applied in the research facility (see Section 5.5.2.1and Section 6.2).Thus,onlyonescreen option is evaluated and compared to the reference situation (without a screen). If a screen ispresent, it is closed when the outside air temperature drops below 8 °C,which is acustomary closing condition for nurseries that intensively apply a thermal screen. After a closure, the screen starts to open 20 minutes before sunrise and, after having paused three times at intermediate positions, is fully opened at sunrise. In the last two weeks of November, when the canopy is removed from the greenhouse the thermal screen is closed every night. When a screen is present in the greenhouse, the interception of radiation by constructionelementswithinthegreenhouseenclosure(thevariableaobsinSection 5.5.2.4) is enlarged to 10%(against 6% for the reference greenhouse). The daily heat consumption for the reference greenhouse with and without a screen areshowed inFigure 6.26.Ofcoursetheenergysavingeffect ofthescreen is limited tothe coldperiod oftheyear, becausethe screen only closeswhenthe outside temperature drops below 8 °C. The year round decrement of energy consumption was 0.47 GJm"2year"' (23%).  14  Dailyenergyconsumption [MJnv2]     witha screen  ' dec ' jan ' feb ' mar ' apr ' may ' jun ' Jul ' aug ' sep ' oct ' nov ' Figure 6.26Dailyheatdemandofagreenhousewith,andagreenhouse without anoverheadthermal screen. The negative impact onbiomass production ofthe increased interception of light bytheconstruction relatedtothethermal screen isshowedinFigure6.27.Insum136  Evaluation of energy saving techniques  mer, where the amount of light is large, the decrease of photosynthesis is limited due to the non-linear response of photosynthesis on radiation level. In winter, the relative decrement of photosynthesis is even more than the relative increment of obstructing elements, although thephotosynthetic response on radiation is about linear at low radiation levels. This is caused by the larger impact of the dark respiration on the daily photosynthesis.  Relative photosynthesis  dec ' jan ' feb ' mai '  Figure 6.27 Relative daily dry matter photosynthesis of a greenhouse with a thermal screen compared to a greenhouse without a screen. Indeed, Figure 6.27 shows that in winter the relative photosynthetic activity in the greenhouse with a screen drops to 6% (whereas the screen isassumed to intercept 4% of the solar radiation) of the photosynthetic activity of the reference greenhouse. In summer the decrement of assimilation rate is about 3%. As argued in the introduction to this section, the energy saving of the thermal screen is corrected for this decrement of production by representing the savings in terms of specific energy consumption, expressed inMJkg"1.This resulted in the figures presented in Table 6.5 Table 6.5 Specific energy saving of a greenhouse with an overhead screen compared to the reference greenhouse  reference greenhouse with thermal screen  energy consumption MJkg-1 218 175  portion for dehum. MJkg' % 24 n 26 15  spec, energy saving MJkg 1 % 43  20  137  Results From Table 6.5 itcanbeseenthatthespecific energy savingduetothe described application ofanLS-10+ screen is43MJkg"1,which is20%ofthespecific energy consumption of the reference greenhouse. Because the screen obstructs moisture transport to the cover, the uncontrolled moisture lossdecreases in favour tocontrolled dehumidification. In agreenhouse with a thermal screen the humidity is controlled in first instance by opening the screen somewhat. Only when the humidity remains at anunacceptable high level after thescreen hasbeen opened,arethewindows opened.However, thiswill not occur frequently because, as soon as the screen is opened a little, large amounts of vapour can condense against the cover, due to its low temperature. Thus, because the number of occasions that the windows have to be opened to carry off vapour is comparable for agreenhouse with and a greenhouse without a thermal screen,theabsoluteportionsofthespecific energy consumption for dehumidification are about the same (240 GJm*2year~' and 220 GJm"2year"' respectively). However, due to the specific energy decrement of 20% the relative portion of energy consumption for dehumidification is larger for the greenhouse with a thermal screen.  Coated cladding material Becauseofthehightransmissivity for shortwaveradiation andthelongdurability, as far as greenhouses are concerned, glass isthe cladding material most applied in the Netherlands. However, on days with clear skies,theradiative heat lossof aglass-covered greenhousecanbequite largeduetothehighemission coefficient of glass for thermal radiation. Coated glassmay reduce theemission coefficient. Currently, HORTIPLUS® isthe only coated glass paneused in horticulture. The emission coefficient for thermal radiation of HORTIPLUS, providing the glass is dry, is 0.25 (0.84 for ordinary glass) (Out & Breuer, 1995). During rainfall, the effect of the coating vanishes. Thus, if the effect of rainfall on the emission coefficient isneglected, the energy-saving effect of this coating willbeover-estimated. However,duringrainyperiodstheskytemperature willbe about equal totheairtemperature andtherefore the effects oftheneglection will besmall. Model computations showed that, when therain effect isnottaken into account, the resulting energy consumption of the greenhouse is 3%less than the energy consumption computed for the greenhouse when the rain-effect has been taking into account. Fortunately, information on rainfall is present in the SELyear. Thus the rain-effect could be included in the model. The decrement of yearly primary energy consumption due to the application of 2 HORTIPLUS was computed to be 0.36 GJm" year"' (18%). An important disadvantage of HORTIPLUS is the diminished transmissivity for 138  Evaluationofenergysaving techniques short-waveradiation.InFigure6.28thetransmission andreflection coefficient for short-wave radiation of both ordinary glass andHORTIPLUS are shown as a function of the angle of incidence. [-]  0.8 0.6ordinary glass Hortiplus®  0.40.2  10  20  30  60 70 80 90 angle ofincidence [°]  Figure 6.28 T and p for short-wave radiation of both ordinary glass and HORTIPLUSasafunction oftheangleof incidence (computedwith the theorypresented by Out&Breuer, 1995). Themodel tocomputethetransmissivity ofagreenhouse covering structure,presented in Appendix C, showed that, due to the application of HORTIPLUS, the transmissivity of the reference greenhouse for diffuse radiation from a standard overcast skydropped from 0.79to0.70.Thedirect transmissivity figures dropped about 11% aswell (although somewhat more for low elevation angles). Duetothereduced amount of light insidethegreenhouse,thebiomass production was reduced. The mean decrement of production appeared to be 12% in winter and about 7% in summer. The simulation model computed the yearly photosynthesis inthe reference greenhouse cladded with HORTIPLUS on 0.92 compared to the greenhouse cladded with ordinary glass. Theeffects ofHORTIPLUSonthespecific energy consumption, taking account for the decrement ofproduction isshown inTable 6.6. Thetable shows thatthespecific energy saving effect of HORTIPLUS is limited to 10%.An important reason for the small effect is the amount of energy required for dehumidification. The large portion of the energy consumption for dehumidification (38.3 MJkg'1 or 325MJm"2year"') iscaused bythe fact that condensation atthecoated coveris much lessthanthecondensation atanordinary cover.Thisisaresult ofthehigher glass temperature of coated cladding material, due to the reduced radiative heat loss.Tocompensate for areduced condensation, thegreenhouse withHORTIPLUS 139  Results hasto carry off moisture by means of ventilation. This way of dehumidification requires more energy because, when ventilating, both latent and sensible heat is lost to the atmosphere. Table 6.6Specificenergyconsumptionandspecificenergysavingofagreenhouse claddedwithHORTIPLUS compared to thereference greenhouse.  reference HORTIPLUS  energy consumption MJkg-' 218 195  portion for dehum. MJkg-' % 24 11 38 20  spec, energy saving MJkg' % 23  10  Double glazing Besidestheapplication ofcoated glasspanes,theheat lossatthecover canbereduced by other measures aswell. Double glazing is one of those options. Tocomputetheeffect ofdoubleglazingonenergy consumption andphotosynthesis the greenhouse climate simulation model has been extended with a second glass pane. This meant that a state variable (Tcov2) and two heat fluxes (HCovCov andRcovCov) w e r e added tothethermal sub-model. Intheextended model, thenet fluxto Tcov changes in (compare with Eqn. 5.29): H  cov,net  =  P  SunCov + H To P Cov + H AirCov + R FIrCov + R L  S c r C o v + R UppCov+  R  tWm"2J ( 6 2 )  L o w C o v + ^anCov" 1 "  CovTop + L AirCov ~ H CovCov - ^ o v C o v  The net flux to the upper glass pane was stated by: H  cov2,net  =  P  SunCov2 + H CovCov H  +  ^ovCov ~  [ W i n 2 ] (6.3)  CovOut ~ ^ o v S k y  The derivative dT^j/dt wascomputed analogue to Eqn. 5.28. The forced fluxes PsunCovand PSunCov2 were computed by: P P  SunCov = a cov 0 - a c o v ) ^ l o b SunCov2 = *cov Iglob  [ W m ' ? l <6-4> ^ 1 (6-5)  To account for the doubled obstruction ofthe glasspanes, for thediffuse anddirect transmissivity the values of Tdirand idif, as defined in Section 5.5.2.4 were squared. Theconvective heatexchangecoefficient HECCovCov wassetto3Wm"2K"',which was mentioned by Schinkels (1980) to be a customary value for ordinary double glasspanes.The radiative heat exchange coefficient (RECCovCov)was determined 140  Evaluationofenergysaving techniques by theapplication of Equation E.7, using an emission coefficient of 0.84 (Out & Breuer, 1994). After having extended the simulation model, computations were carried out to determinetheenergy savingandbiomassproduction effects. Theresultsarestated in Table 6.7 Table6.7Specificenergyconsumptionandspecificenergysavingofagreenhouse witha double glasscoveringcomparedtothereference greenhouse  reference Double glass  energy consumption MJkg-1 218 175  portion for dehum. MJkg-1 % 24 11 49 28  spec, energy saving MJkg' % 43  20  For thedouble glazed cover, themodel computed thattheyearly energy demand dropped to 1.36 MJm"2year"' and that the photosynthesis dropped with a factor 0.16. Still the specific energy saving(43 MJkg"1)isalmost doubled, compared to the former alternative. In line with the tendency in the former cases that the relative portion of energy consumption for dehumidification increases for better insulated buildings, the double glass cover applies almost 30% of its energy consumption for humidity control (49MJkg"1or380MJm'2year"').Thishighproportion iscausedbythe fact that in a double glazed greenhouse, there ishardly any condensation.  Polymer coating  Inthework ofOut &Breuer (1995) applications ofpolymer coatingswerementioned asimprovingtheopticalproperties ofglass.Thesecoatingsdonotdecrease the long-wave emissivity, but increasetheshort-wave transmissivity (by decreasing the reflection coefficient). This property appeared not to be affected when suchapolymer isaddedtoaglasspanewithanoxidecoatingsuchas HORTIPLUS. Samples of glass panes with such a double coating were tested by Out & Breuer andtheyreported thatthesesampleshadashort-wavediffuse transmissivity, comparable tothediffuse transmissivity ofordinary glass,whilethelong-wave emission coefficient remained 0.25. Another possibility is to add the polymer coating onto clear glass to be used in doubleglassconstructions.Intheapplication proposedbyOut&Breuer,thecoated sides ofthe glasspaneswere facing each other. In doing so,they reported the transmissivity of a double glass pane to be about equal to the short-wave transmissivity of an ordinary single glasspane. Athird possibility is to construct a double glass pane from panesthat each have a double coating. This cladding material has the light transmission properties of 141  Results ordinary double glass, discussed in the former item, but the radiative heat exchangecoefficient RECCovCov becomes afactor 0.2 compared totheradiativeheat exchange between the untreated glass panes. In Table 6.8, the results of the effects of the polymer coating for all three applications is listed. Table6.8Specificenergyconsumptionandspecificenergysavingofagreenhouse with various applications of polymer coatings compared to the reference greenhouse.  reference HORTlPLUS+polymer coating coated double glass double-coated double glass  energy consump. MJkg 1 218 178 151 134  portion for dehum. MJkg-1 %  spec.en.saving MJkg' %  24 36 41 53  40 67 84  11 20 27 40  Thetable shows another increment of the energy savings, compared to the cases discussed previously. It is interesting to see that the absolute portions of energy for dehumidification for the first and second application of the polymer coating is less than the portions computed in the former cases. This effect must beattributed totheincreased entranceofsolarradiation intothegreenhouse.Thus,inthe polymer coatedgreenhouses thelatentandsensibleheat losstotheatmosphereby ventilation is more often derived from the sun, than from the heating system. Theenergy consumption related todehumidification perm2greenhousewascomputedtobe330MJm"2year"' fortheHORTlPLUS+polymercoating,460MJm"2year"' for the coated double glass and 670 MJm"2year"' for the double-coated double glass.  Conclusions  Theeffect onenergyconsumption ofwindowsthat,duetotheslovenly adjustment of their mechanisms, remain a little open when they were meant to be closed, is small. When20%ofthewindows haveanopeningof 1 cm, theenergyconsumption of the greenhouse is only 1.6%more than the energy consumption itwould have when the ventilation mechanism was well adjusted. The other measures which can beused to diminish the heat losses from thebuilding, and which were studied in this section, can affect biomass production throughadiminished transparency ofthegreenhouse.Themodelcomputeddecrements ofphotosynthesis between 3%(a thermal screen) and 16%(double glass). Theeffect ofproduction losswastaken intoaccountbyjudgingtheenergy saving measures on specific energy consumption, defined as the yearly primary energy 142  18 31 39  Evaluationof energysaving techniques consumption divided by the yearly sum of photosynthesis. The results showed specific energy savings ranging form 10%(HORTIPLUS)to 39% (double-coated double glass). Besides information onthe specific energy savings of alternative claddingmaterials and the thermal screen, the simulation model has been used to compute the portion ofthetotal energy demand required for dehumidification. Itappearedthat adecreasing heatlossthroughthecovering structure resulted inagrowingportion of the primary energy demand being required for humidity control. For HORTIPLUS thisportion is20%(325 MJm^year"1), but for the greenhouse covered with double-coated doubleglass,40%oftheenergy consumption isrelatedtohumidity control(460MJm"2year"').Thereference greenhouseuses 11%(220MJm"2year"') of its energy consumption for dehumidification. From the growing amount of energy consumed for dehumidification, itcanbeconcluded thatthedecrement of energy consumption of greenhouses can (highly) be over-estimated if dehumidification is not taken into account.  6.3.4.3 Energy conservingheatingdevices. Tocovertheheatdemandofgreenhouses,primary energyhastobeconverted into heat.Also,toenhanceproduction,naturalgasiscombustedtoproduceC0 2 .Finally, primary energy is applied to produce electricity. Thus, in horticulture, three conversion processes with respect to natural gas (the conversion to heat, to C0 2 andto electricity) can bedistinguished. An increased efficiency ofthese conversion processes serves the target of energy conservation. The condenser enhancestheconversion process of natural gastoheat.The effect ofacondenser willbestudiedbymaking acomparison ofagreenhousewithsuch a device (the reference greenhouse) with one that omits a condenser. Moreover, apart from thereference connection (see Figure 4.3) an alternative connection of the condenser to the heating system will be analyzed. Theheat storage tank isan important deviceto savethereject heat from theconversion of natural gas to C0 2 and to electricity. Thus, in fact it enhances these conversion processes.Theeffects of such astorage tank are studied asa function of its storage capacity. The combined heat andpower engine isthe third energy conserving heating device.Thisdevice contributestoenergy savingbecause itimproves theconversion efficiency of natural gas to electricity by enabling the application of the reject heat.However, for thisdevice,thebenefits areonlynoticed whenprimary energy saving elsewhere is attributed to the electricity production in the greenhouse.  143  Results Condenser Inmost greenhouses thecondenser isconnected toaheatingcircuit which ispreferably applied by this heating device only (Van der Velden, 1995). In the reference greenhouse,theupperheating circuit servesthis function. Only duringcold periods,whenthetemperature setpointofthelowerheatingcircuit exceeds 55°C, hot water ispassed to the upper heating circuit, taking the decreasing efficiency of the condenser for granted. The condenser is apart of the heating system of thereference greenhouse. Thus the energy savings of the device can be studied by removing thecondenser from theheatingsystem andthen comparing theyearly heatdemand computed by asimulationwithoutthecondenser withthe2.013GJm"2year"'thatholdsfor thereference greenhouse. In thereference greenhouse,thecondenser isconnected totheupper heatingsystem (see Chapter 4).This means that return water from the upper heating circuit isledthroughthecondenser. Thecondenserheatsthiswaterandpushesitintothe supply side of the upper heating circuit. However, in this configuration, during periods where theheat demand is governed by aminimum pipetemperature, the heat gained from the exhaust gases is not used in anefficient way, because only the lower heating circuit requires heating power. Therefore, the performance of thecondenser isstudied in analternative configuration aswell.Inthis alternative configuration, duringperiods wheretheminimum pipetemperature constrains the temperature of thelowerheating circuit, thewater tothecondenser iswithdrawn from thereturn pipe of the lower heating circuit. Thus the condenser contributes to theheat demand of the lower heating circuit. The condenser switches back to the upper heating circuit when the setpoint for the lower heating circuit exceeds theactual minimum pipe temperature with 1°C.Thehydraulic scheme that enables this alternative control of the condenser is shown in Figure 6.29. In the alternative configuration, the valve that controls the selection between the one or the other heating circuit is always moved to one oftheextreme positions. Theresultsofthemodel computation for thegreenhousewithout acondenserand for theheatingsystemwiththealternative heatingsystem configuration arestated in Table 6.9. Theboiler was assumed to betuned onan air factor (X)of 1.2(see Section 4.3.4.1). Thecomputationsshowthatthecondenser inthereference configuration saves7% compared toagreenhousewithoutacondenser. Withthealternative configuration the savings are increased to 9%. This means that if the heat demand is not governed by the realisation of a greenhouse air temperature, feeding the condenser withrelatively warm water (return water from thelowerheatingcircuit insteadof the upper heating circuit) is advantageous, in spite of a diminished condenser efficiency.  144  Evaluationof energysaving techniques condenser  from -boiler -CHP •buffer  condenser  -v-  to -boiler -CHP -buffer  - < * upper heating circuit  lower heating circuit  reference configuration  from -boiler -CHP -buffer  to  -boiler -CHP -buffer  $  n  32 I  I  <&-  upper heating circuit  <$"  lower heating circuit  alternative configuration  Figure6.29. Hydraulic schemeofthereference andalternative connection ofthe condensertotheheatheating circuits. Table 6.9Yearlyenergyconsumption ofthereference heatingsystem(witha condenser) anda heating system with analternativeconnectionofthe condenser,comparedtoagreenhouse withouta condenser. energy consumption GJm"2year"'  energy saving MJkg"1 %  greenhouse without condenser  2.165  reference greenhouse  2.013  151  7  greenhouse with alternative condenser configuration  1.973  192  9  -  Asanillustration, Figure 6.30 showsthedecrement ofmean condenser efficiency in the alternative configuration compared, tothe reference configuration. Inthis Figure, anefficiency 1means that allheat which ispresent inthe exhaust gases, relative tothe heat content ofthe ambient airisgathered (like inFig.4.13). From thedatashown inFigure 6.30 itwascomputed thatthemeanconversion efficiency ofthecondenserwas0.77forthereference configuration and0.74forthe alternative configuration. Figure 6.30shows that thecondenser runs atan efficiency ofbetween 0.75 and 0.85 formostofthe time.From Figure 4.13itcanbe seen that, toreach such anefficiency, thewater fedtothecondenser has to be below35°C.Indeed, asshown inFigure 6.22,thetemperature ofthereturnwater of theupper heating circuit hardly exceeds atemperature excess of 15°Cabove the greenhouse airtemperature. The lowefficiencies at 0.25and0.30originate from periods with a high heat demand, where theupper heating circuit acts asasecondary circuit.  145  Results Hours 2500-  2000  alternative configuration  1500-   1000reference configuration  sooI  I  ~  I  fl  '  t  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 condenser efficiency [-]  |]|lyfiflfljfl|l|'  Figure 6.30 Frequency distribution of condenser efficiencies. The condenser efficiency expresses thefraction of heat recovered from the heat content of the exhaust gases.  Short-term heat storage A short-term heat storage facility saves energy if it carries heat from aperiod with heat surpluses to a period with a heat demand. The energy is stored as hot water in a tank (see Section 4.4.6). In the present heating system, heat surpluses can be caused by the boiler, when it runs to produce C0 2 , or by the reject heat of electricity production by combined heat and power. The energy conservation achieved with aheat storage tank depends onthe alternative for storage. If heat production can be decreased when it exceeds the demand (by stopping the CHP engine or the C 0 2 production), a storage tank does not conserve energy, but, as will be shown, has other advantages. If the alternative to storage istoraise theheat supply tothe greenhouse, forcing additional ventilation, the temporary storage of heat avoids energy losses. With respect to C 0 2 production, the fact whether astorage tank saves primary energy depends on the C 0 2 supply strategy. In the reference supply strategy (see Section 6.3.1), C 0 2 production isstopped when the greenhouse lacks a (sufficient) heat demand. Thus, the heat storage tank does not contribute to the decrement of primary energy consumption inthe reference greenhouse. Rather, the storage tank affects specific energy consumption because, since it can absorb heat surpluses, the C 0 2 supply can be increased (resulting in an increased photosynthesis). However, in present horticulture it is also quite common to supply C 0 2 irrespective of 146  Evaluation of energysaving techniques the heat demand. In that situation a heat storage tank serves the energy conservation objective.Moreover, aswill beshown, itevenslightly enhances photosynthesis. The effects of the storage tank on yearly absolute energy consumption, yearlyphotosynthesisandspecific energyconsumptionwillbestudied for boththe supply strategies. When aheat storage tank isused ingreenhouses with artificial illumination poweredbyCHP,the storage tank isusedbyboththeCHPengine(when itisswitchedon for lighting)andtheboiler (whenproducing C0 2 ).ACHP engineonbehalf ofartificial lightingisnormallyoperatedirrespectivetheheatdemand,becausethe illumination controller has the highest priority. Thus, with respect to heat surpluses, this case is comparable to the second C0 2 supply strategy (C0 2 supply irrespective oftheheatdemand).Consequently,thestoragetankwillhaveanenergysaving effect. However, becausethe storage tank canbeused bytheboiler as well,providing thereference C0 2 supply strategy isapplied (C0 2 supply aslong asthereject heatcanbeusedorstored),anincreasingheatstoragetankwillresult inan increment ofC0 2 supply.Thus, againthe effects ofthe storage tank canbe judged with respect to absolute energy consumption, yearly photosynthesis and specific energy consumption. When CHPisusedtoproduce electricity for thepublicgrid (discussed inthenext section), the device normally does not produce surpluses, because it is common practice to stopthe enginewhen theheat demand istoo small (Oversloot, 1992).  Effectsofa storagetank inrelationto C02 supply To study the effects of heat storage in relation to C0 2 supply, again the horticultural contextofthegreenhouse growingtomatoesused intheprevious sections servesasareference. However,tostudytheeffects for bothextremeswithrespect to C0 2 supply strategies (stopping the supply when there is no heat demand or C0 2supplyirrespective oftheheatdemand),besidesthereference supplystrategy, the simulation model was employed using the second C0 2 supply strategy. Simulations were carried out for 6storage tank values (5,20,40,60, 80and 100 m3ha"') for boththesupply strategies andthreeexhaust gassupplyrates.Thesupply rateswere settoacombustion of 25, 50and 75m3 of natural gasper hectare perhour.Thefirstvalue islessthanthesupplyrateusedinthereference situation (40 nrWhr" 1 , see Section 6.3.1). The highest supply rate is significantly more, but certainly not unusual in present horticultural practice. Figure 6.31 and 6.32 show the results with respect to energy consumption and yearly photosynthesis. Figure 6.31clearly showsthat aheat storagetank decreases theenergy consumption only when the second supply strategy isapplied. This could be expectedbecause the storage tank prevents reject heat being carried off by increased venti147  Results  lation. The larger the tank, the more heat surpluses can be absorbed. Of course, in the second supply strategy, the amount of heat to be carried off is greater when the supply rate is higher. Thus the effects of a heat storage tank are larger for increasing supply rates. Energy consumption [GJm'2year'] 2.4  second supply strategy A 75m3ha 'hr 1 • 50m3ha'>"-'  2.3  2.2  2.1  reference supply strategy*' 1.9 10  20  30  40  50  60  70  80  90  100 110  storage dimension [m3ha'] Figure 6.31Energy consumption of the reference greenhouse as afunction of heat storage dimension for three levels of C02 supply and for two supply strategies. The reference supply strategy prohibits the combustion of gasfor CO2 supply when the greenhouse lacks a heat demand and the storage tank is completely filled. The second strategy supplies C02 irrespective of the heat demand. Figure 6.31shows that thetank does not yield an energy conservation for the reference supply strategy. The energy consumption can even be seen to increase with the storage tank dimension. This increment is caused by an increased energy loss from thestoragetank.Again theeffect, which isan increment ofenergy consumption this time, is greater for higher supply rates. Of course the increased energy losswill occur with respect to the second strategy as well, but that cannot be seen inthe graph because the increased losses are lessthan the savings from the storage tank. Figure 6.32 shows that the effect of the storage tank dimension is much larger for the reference supply strategy than for the second strategy as far as photosynthesis is concerned. The results of the reference strategy differ significantly from the results of the second strategy for a particular supply rate for low storage tank dimensions. This is caused by the fact that, for the reference strategy, the amount of C 0 2 that can be supplied is strongly limited by the heat demand in the period 148  Evaluation of energy saving techniques  that the boiler produces C 0 2 (the daytime). As the dimension of the storage tank increases, the differences between the strategies become smaller. If the storage tank is so large that it can always absorb the heat surpluses, the C 0 2 supply is never prohibited for both supply strategies. However, for the highest supply rate, even for the largest storage tank adifference between the supply strategies persist. Moreover, the difference will remain even when the tank becomes larger because it can be seen from the figure that the dashed curve for the 75 m3ha',hr"1 supply rate has almost flattened out. It can be deduced from this fact that the daily amount of heat produced by a boiler for that supply rate exceeds the diurnal demand. Indeed, the combustion of 75 m3ha"'hr"1 during some 16 hours (in summer) yields 3.8 MJ, whereas the mean daily consumption in summer for the reference greenhouse is less than 3 MJ (see for instance Figure 6.26). Also remarkable in Figure 6.32 is the declining increment of photosynthesis for the increasing level of C 0 2 supply rate. Finally, the figure shows that for the second strategy too,theyearly photosynthesis increases for increasing storage tank dimensions, especially for the highest supply rate. This is caused by diminished losses of C 0 2 because extra ventilation, carrying off reject heat, is needed less frequently as the storage tank increases in size. Yearly photosynthesis [kgm2year'] 10__ _ _ - -A-  9.5  • ^St-X-  -•SOm'ha-'hr1  -A"""  -X  v", *  -*-  -X-  25m3ha 'hr'  8.5'  reference supply strategy second strategy 7.5  1  1  i '  10  20  ' i ''  T1-  30  40  1  50  1  i'  60  70  i '  80 90 80  100 110  storage dimension [m3ha'] Figure 6.32 Yearlyphotosynthesis of a tomato crop as afunction of heat storage dimension for three levels ofC02 supply andfor two supply strategies. As in Section 6.3.4.2, the effects of photosynthetic activity and energy consumption can be combined into a single number describing specific energy consumption. This number is shown as a function of the storage facility dimension in Figure 6.33 for both extremes. 149  Results Specific energy consumption [MJkg'] 0.26 ; 0.25 H  „reference supply strategy  v/  A 75m3ha 'hr' • 50m3ha'hr ' X 25m3ha 'hr'  0.24 0.23 second supply strategy 0.22 ^ 0.21 0.2  > i •  10  20  30  40  50  60  90 110 70 80 90 100 storage dimension [m3ha']  Figure 6.33 Specific energy consumption of the reference greenhouse as a function of heat storage dimension for three levels ofC02 supply and for two supply strategies. All curves in Figure 6.33 tend to decrease when the heat storage tank increases. Also,itappears thatthe supply strategy becomes less important for increasing heat storage tanks. The decrement of specific energy consumption ranges up to 20% for the reference C 0 2 supply strategy. For small storage tanks the second supply strategy yields a significantly lower specific energy consumption than thereference strategy. Moreover, thesupply rate at 50m3ha"'hr'1 yields the lowest value for that supply strategy, unless the storage tank exceeds 80 m3ha"'. This must be attributed to the declining extra photosynthesis (see Figure 6.32) when the supply rate is increased. In general, the supply of C 0 2 irrespective of the heat demand results in the lowest energy demand per unit of photosynthesis. However, when the storage tank exceeds 70 m3ha"', the highest supply rate starts to yield the lower specific energy consumption, providing the reference supply strategy is applied.  Effects of heat storage for a greenhouse with a CHP engine for artificial lighting A greenhouse growing roses with artificial illumination was simulated to study the effect of heat storage with respect to combined heat and power for private electricity production. Except for the illumination, the greenhouse construction was assumed to be the same as the one hectare greenhouse that served as a reference in the preceding sections. Illumination was applied between 8 August and 27 150  Evaluationof energysaving techniques April.Thelampswereswitchedonwhenoutsidesolarradiationintensity dropped below 75Wm"2.Duringtheperiod from one hour before sunset till 5hours after sunset the lamps were not allowed to be switched on. This illumination control strategy was equivalent to the strategy applied in the research facility discussed inSection 6.2.1.Usingthisstrategy,artificial illumination isinusefor about3000 hours per year (3041 hours in the SEL-year) in the Netherlands. Byassumingthesame amount ofluminaires perm2asintheresearch facility, artificial lighting consumes 44 Wm'2 of electrical power. Typically, a CHP engine asapplied inhorticulture, hasathermal power which isa factor 1.6ofitselectric power (Klimstra, 1991). This yields a thermal power of 70Wm"2. The airtemperature setpointswere setto 19°Cduring daytime and 17°C for the night, throughout the year. The light dependent temperature setpoint increment was parametrized according to the settings mentioned in Section 6.3.1. From 1 April to 1 October, the minimum pipetemperature for the lower heating circuit was 45 °C during the day and 40 °C during the night. At high levels of solar radiation, theminimum pipetemperature was lowered according tothesettings mentioned in Section 6.3.1. The humidity setpoint was 85%RH except for theperiod between 1September to 1 December, where the setpoint was lowered to80%RH.C0 2wassuppliedbycombustingnatural gasatarateof40m3ha"1hr"1. The C0 2 supply was stopped whenthe greenhouse lacked aheat demand andthe storage tank was completely charged. Withthesettingsmentioned above,theclimate controller setpoints for the growth ofroses are comparable tothesettings for thetomatocrop,except for thesettings holding for the period when the tomato crop was removed and the first three weeksafter anewcrop isplanted.Thisperiod runs from 11November to21December. Asinthecaseofthegreenhouse growingtomatoes,thenursery growingroseswas supposed not to have athermal screen. The effect of the storage tank was determined by simulating year round energy consumption andphotosynthesis for the samesixstoragetankvolumes applied in the former section. Theresults ofthe simulations withrespect toprimary energy consumption, yearly photosynthesis and specific energy consumption are shown in the Figures 6.34, 6.35 and 6.36 respectively. The fact that anincreased storage tank savesprimary energy showsthattheCHP engineproducesheatirrespectiveoftheheatdemand.However,becausethedecrementoftheprimary energyconsumption issmall (for thelargestheatstoragetank about 7% of the energy consumed when the greenhouse is not equipped with a heat storage tank), the heat surpluses caused by the combined heat and power engine are limited.  151  Results Energy consumption [GJnr2year']  ••'' 1 1 i i 1 1 i • i i i i 1 1 1 1 i i i i 1 1 i i i i i 1 1 i 1 1 i i i i  0  10  20  30  40  50  60  70  i i 1 1  80  1  | | 1 1  90  1  100 110  storage dimension [m3ha'] Figure 6.34 Primary energy consumption of agreenhouse using artificial lighting powered by on-site CHP as afunction of heat storage dimension. Yearlyphotosynthesis [kgm'year 1 ]  i 11 i i i 11 i i i i i i 11 i i i i i i i i i i i i i i i  0  10  20  30  40  50  60  70  80  90  100 110  storage dimension [m3ha'] Figure 6.35 Yearlyphotosynthesis of an illuminated rose canopy as afunction of heat storage dimension. C02 is supplied according to the reference strategy (stopping the supply if the greenhouse lacks a heat demand and the storage tank is completely fdled). As can be seen in Figure 6.35, with respect to yearly photosynthesis, the storage tank has a considerable impact (up to 18%). The curve inFigure 6.35 is compara152  Evaluationof energysaving techniques ble to the dashed curve for the 50 m3ha"1hr"1 supply rate in Figure 6.32. This is not surprising, since it describes the same effect. However, the curve of Figure 6.35 lies about 0.5 kgm"2year"' higher. This is caused by the fact that the rose canopy grows throughout the year, whereas the tomato hardly assimilates when it isjust planted and is removed from the greenhouse in November. Again, the figures for energy consumption and production can be combined to yieldthespecific energyconsumption.Thespecific energy consumption isshown in Figure 6.36. Obviously, the application of a large storage tank reduces the specific energy consumption by some 20%. This Figure is comparable to the decrement achievedwhenthestoragetank isapplied for surpluses from theboiler due to C0 2 supply. Figure 6.36 also shows that the level of thecurve is significantly higher thanthe levels of the curves presented in Figure 6.32. This is caused by the fact that the applicationofartificial illuminationresultsinhighprimary energydemands.However, aswill be discussed in the next section, if the lamps were powered by the public grid, the actual primary energy consumption would be even higher. This isbecause then the primary energy applied by the power plant that produces the electricity should be taken into account. Specific energy consumption [MJkg'] 0.32  0.28  0.26  i i '' ' i ' '' ' i ''' ' i '' '' i ' ''' i ' ' '' i ' ''' i ''' ' i ''' ' i '' ''  0  10 20 30 40 50 60  70 80 90 100 110 storage dimension [m3ha']  Figure6.36Specificenergyconsumption ofagreenhouseusingartificial illuminationasafunction of heatstorage dimension.  153  Results Combined heat and power Application of combined heat and power at a nursery raises its primary energy consumption. However,theelectricityproduced replaces electricity production of large power plants. Because, unlike the case with CHP, as a rule the reject heat of those large power plants isnot used, on anational scale,the energy conservation objective can still be served. Of course the net effect of CHP depends on the conversion efficiencies of the production processes compared. The decrease of natural gas consumption in a power plant per unit of electric energy produced with on-site CHP can be expressed by: G  P-,PP =" n p p 3 5 W  ^ <6-6>  inwhich Gprimpprepresents the (decrease of) gasconsumption atthe power plant (m3), Echptheelectricity production bycombined heatandpower(J),rpp theconversion efficiency ofthepowerplantand 35.16-106theupperheatingvalueofnatural gas of Slochteren quality at standard pressure and temperature (Jm"3). For modern gasfiredpowerplantstheconversion efficiency isabout0.45oftheupper heating value (0.5 of the lower heating value). The year round electricity production of a CHP engine is (providing the engine runs on full capacity only)the product of electric power andthenumber of runninghours.Inahorticultural contextthenumber ofrunninghoursdependsmainly on the thermal power of the engine. To determine the relation between thermal power and the number of running hours the simulation model has been applied for 5 levels of thermal power (20, 40, 60, 80 and 100 W^m"2). The horticultural context ofthe simulations wasdescribed by the reference greenhouse and its set of horticultural settings (see Section 6.3.1, 6.3.2 and 6.3.3). To get an impression ofthe contribution of CHP toheatproduction the mean dailyheatproduction oftheengines isshown inFig. 6.37. The horticultural context is included in the figure by the grey shaded total mean daily heat demand of the greenhouse. The fact that even the engine of 100W^m'2 never covers the total heat demand isattributed tothecarbon dioxide supply,which forces theboilertoproduce heat. Also, during peak heat demands, which cannot be seen in the figure because of thesmoothingsthatwereappliedtothedata(a 10cellsmovingaveragefilter),the boiler suppliesheatnow andthen.Obviously, insummer theheat associated with C0 2 supply severely diminishes the contribution of CHP. Therelative contribution oftheheatingdevices ingreenhouse heatproduction are tabulated in Table 6.11. Thetable clearly showsthedecreasing additional contribution oftheCHP engine asthe thermal power becomes greater. The amount of heat released by C0 2 pro154  Evaluationof energysaving techniques duction isconstant,becausetheC0 2 supplyhasahigherpriority thantheproduction of electricity. The increment of the contribution of the condenser is caused by the higher amount of exhaust gases per unit of thermal energy from a CHP engine,compared totheamount ofexhaustgasesper unitofthermal energy from a boiler.  Meanheat demand/production [Wm!] 120  100 Wu.m dailyheatdemand  1  aug ' sep '  Figure6.37Dailyheatdemandof thereference greenhouseanddaily heatproduction of CHPfor 5 thermalpower levels. In order to present a readablepicture the daily meanvalueswere smoothed by a 10 cells movingaveragefdter. Table 6.11 Totalyearlyheatproductionoftheheatingdevices andthepercentage of contributionfor the referencegreenhouse with 5 differently sized CHP engines. thermal power fWm-2l 0  20  40  60  80  100  CHP  0  20%  36%  49%  58%  63%  boiler  70%  49%  32%  19%  9%  4%  condenser  10%  11%  12%  12%  13%  13%  C0 2 supply  20%  20%  20%  20%  20%  20%  total  100%  100%  100%  100%  100%  100%  To compute the extra gas consumption andthe electricity production for thefive casesathermal andanelectricconversionefficiency mustbeemployed.Typically, thethermal conversion efficiency ofcurrently appliedenginesis0.47withrespect 155  Results  to the upper heating value (0.53 with respect to the lower heating value). The electric conversion efficiency is typically a factor 1.6 smaller (Klimstra, 1991). From thetotalheatproduced bytheCHPengine,ascomputedwiththemodel,the electricity production can becomputed and,bymeans ofEqn. 6.6,thesavings of natural gas at the power plant. The gas consumption of the CHP engine and the boilercanbecomputedfrom theirconversionefficiencies whicharethepreviously mentioned 0.47 and 0.85 with respect to the upper heating value of natural gas. Table 6.12 shows the electricity production, gas consumption of the nursery, savings atthepowerplant andnet savings ofnatural gas for thefivelevels of thermal power. Table6.12Electricityproduction,gas consumption ofthenursery, savingsatthe power plant and net savings of naturalgasfor five thermal power levels. thermal power [Wm'2] electricity production [MJm"2] nursery gas consumption [m3m"2year''] power plant gas saving [m3m'2year''] net energy consumption [m3m"2year"'] energy saving  00 0 57 0 57 0%  20 20  240 67 15 52 9%  40 433 75 27 47 18%  60 585 80 37 43  25%  80 693 84 44 41 28%  Table6.12 showsthattheapplication ofCHPhasaconsiderableimpact onthegas consumption ofthenursery.However, onanationalscale,thisextragasconsumption isamply compensated bysavingselsewhere.Thus, for alargecombined heat andpowerengine,thenetenergyconsumption dropstolessthan70%oftheenergy consumption of the reference greenhouse. In the control strategy subject to the simulated cases, the CHP engine does not affect canopy growth. Thus,thespecific energy consumption dropsparallel tothe decrement of net energy consumption. The computations show that from March up until the end of the growth season, the contribution to theheating of the greenhouse is less than thepotential contribution for alldevices.This isduetothereject heat from C0 2 supplywhichcauses the CHP engineto switch off. This means that, iftheexhaust gasesoftheengine were clean enough to be used for C0 2 supply, the contribution made by a CHP enginetotheheatdemand canbeincreased strongly.AlookatFigure 6.37shows thatthe CHPengine with athermal power of20W^m"2(12.5 Welm"2)would run almost 8760hours ayear andthe40W^m"2engine (25 Welm'2)would run about 8500hours ayear. With these running hours an electricity production of 390MJ forthe20W^m'2engineand765MJfor the40W^m"2enginewouldbeachieved. 156  100 747 86 47 39 32%  Evaluationofenergysaving techniques Thus, if C0 2 could be supplied from CHP engines, the net energy saving by application of the 20W^m"2 engine would increase from 9%to 16%.For the40 W^m"2enginethenetenergy savingwould increaseto 33%,which iscomparable to the results achieved for the largest engine if C0 2 is supplied with the boiler. Indeed, currently a number of full-scale experiments are being carried out with devices that clean the exhaust gases to such an extent that they can serve as a horticultural C0 2 source.  Conclusions The application of acondenser inthe reference heating system, where the boiler runsataconversion efficiency of0.85withrespecttotheupperheatingvalueand thecondenser isfed withwater from theupperheatingcircuit,resultsinaprimary energy saving of 7%.An alternative configuration, where the condenser was fed with water from the lower heating system during periods where its temperature wasgovernedbyaminimum pipetemperature, increased theprimary energy savingto9%.Thishigher energy savingwasachieved despitethefact thatduetothe alternative configuration the mean condenser efficiency decreased from 0.77 to 0.74. The explanation by the fact that in the reference configuration the heating power of the condenser during periods where the heat demand is governed by a minimum pipe temperature isuseless. Inthe alternative configuration, duetothe valve that enables aconnection of the condenser tothe lower heating circuit, the heatingpower ofthecondenser contributestotheheat demand ofthe lower heating circuit. Thecomputations withrespecttothetwocondenserconfigurations showsthatthe customary recommendation to connect the condenser to a special heating circuit does not necessarily achieves the highest energy saving. This because,when the configuration lacks a connection to the lower heating circuit, the gathered heat during periods where a minimum pipe dominates the temperature of the lower hating circuit isuseless. Theenergy savingeffect ofaheatstoragetankprincipally dependsonthealternative for heat storage. Only if the alternative is to carry off the heat surplus by forcing ahigherpipetemperature, aheatstoragetankwillresultinprimary energy saving. Inthecomputations onthis alternative, the simulations showthat savings of up to 13%can be reached if the surpluses are caused by C0 2 supply by combusting 75 m3 natural gas per hectare per hour irrespective of the heat demand. For lower supplyrates,thesurpluseswithout astoragetankarelessandsoarethe maximal savings. For a supply rate of 50 m3ha",hfl the maximal saving is 10% and for a supply rate of 25 mha' hr"1 the saving is limited to 6%. If thealternative tothestorage ofheat surpluses istoprevent thesurplusbystopping the C0 2 supply, a storage tank can even increase the primary energy con157  Results sumption ofagreenhouse,althoughtheincrement isalwayslessthan2%.Thisincrement ofenergy consumption iscaused bytheheat lossesfrom thestoragetank surface. However, besides an energy saving effect, a heat storage tank affects the yearly photosynthesisaswell.Thiseffect ismostpronounced fortheC0 2 supply strategy that stops the supply on a surplus (the reference supply strategy). Because the storage tank absorbs the surpluses, the availability of a storage tank enlarges the possibilityofsupplyingC0 2 .Thisresultsinanincreasedproduction.Themaximal increment of yearly photosynthesis was computed to be 14%for the low supply rate.Application ofalargeheatstoragetankonthereference supply strategywith asupplyrate of 50m3ha"1hr"1showed aincrement ofphotosynthesis of 25%. The maximal increment of yearly photosynthesis by a heat storage tank in a greenhouseapplyingthereference supply strategy iseven 28%for thehighsupply rate (75 nvWhr" 1 ). For thealternative supply strategy theheat storage tank results in ahigher yearly photosynthesis aswell. This is because, due tothe storage tank, extra ventilation tocarry off surplusesoccurslessfrequently. Thus,thelossof COzwillbelessand photosynthesiswillbeenhanced.However,theeffect ismuchlessthanthe effects described inthe former paragraph. Themaximal increment ofphotosynthesis for alargestoragetankwasonly 2.2%for thehighest and 1.6% for the 50m3ha''hr'' supply rate. For the low supply rate the increment of yearly photosynthesis was not worthmentioning. Theenergysavingfigures andtheincrementofyearlyphotosynthesis canbecombined toa specific energy consumptionfigure,describing the amount of primary energy required per unitofphotosynthesis. Thecomputation ofthisfigureshows that, in general, for thereference growth of atomato canopy, thealternative C0 2 supplystrategy (supply irrespective oftheheatdemand) uses lessprimary energy per unit of photosynthesis than a strategy that stops the supply when the greenhouse lacksaheat demand. Moreover, ifastorage tank isapplied with acapacity lessthan 80m3h"',the 50m3ha"'hr"1supply rate, irrespective of theheat demand, shows a lower specific energy consumption than both the other supply rates. The curves of the specific energy consumption as a function of heat storage dimension showthat, for aparticular supplyrate,thedifferences betweenbothsupply strategies tend todisappear asthe storage tank increases. Only for thehighest supply rate the specific energy consumption of the reference supply strategy appears to yield an even lower specific energy consumption if the heat storage tank dimension exceeds 70 m3ha"'. Thecomputations oftheeffects of aheat storage tank on anursery with artificial illumination powered by an on-site combined heat and power engine showsboth animportant energy savingeffect andanincrement ofyearlyphotosynthesis.The energy saving effect is caused by the fact that the CHP engine runs irrespective 158  Evaluationof energysaving techniques of the heat demand. The production increment is a result of the fact that the storagetank isalsousedbytheboilerwhen itsuppliesC0 2 according tothereference strategy with a supply rate of 40m3ha"1hr"1. Combiningtheenergysavingandproduction increment inthespecific energyconsumption,thedecrement ofspecific energyconsumption appearstorangeupwards to 24%compared to a situation without a storage tank. The application of combined heat and power, enlarges the gas consumption of greenhousessignificantly. However,becausetheelectricityproduced atthegreenhouse site decreases electricity production elsewhere, CHP can still save energy. Thisisthecaseifitsoverall conversion efficiency ofnatural gastoelectricity and heatislargerthantheconversion efficiency ofpublicpowerplants.Sinceagreenhouse applies (most of) the reject heat of aCHP engine, ingeneral this condition will be served. Thus,tocompute theenergy saving from combined heat andpower, thedecrease of energy consumption atpublic power plants duetothe electricity production at thegreenhousesitemustbesubtractedfromtheenergy consumption ofthegreenhouse. This yields energy savings that, depending on the capacity of the CHP engine, range up to 32% for an engine with a thermal power of 100W^m"2. If exhaust gasesofthedevicecanbecleaned sufficiently toallowthemtobeused for C0 2 supply,acomparable saving canbeachievedbyanenginewithathermal power of only 40W^m"2.  6.3.5 Conclusions on the evaluation of energy-saving prospectives Becauseenergyconservingmeasureshavethegreatestimpactonhorticulturalproduction with a high energy demand, the growth of tomato, planted in December and removed inNovember hasbeen chosen as areference. Indeed, the reference greenhouse, described in Sections 6.3.1, 6.3.2 and 6.3.3, has a much higher primary energy input (2.0 GJnT^ear'1) than the average value for horticulture (±1.4 GJm"2year"', see Figure 2.5) in the Netherlands. Three items on energy conservation were studied for this reference greenhouse. The first item concentrates on the boiler house. Three of the energy conserving measures mentioned bytheMJAwith respect totheboilerhouse were evaluated. Because there are still quite anumber of boilers that are poorly insulated in horticultural practice(Velden, 1995),inthefirstplacetheenergy savingswerecomputed for the increment oftheboiler insulationthicknessfrom2cmto6cm.The boiler model showsthat, for a 2.5 MWboiler, this measure decreases the yearly energy loss from the boiler with 76GJ.For thereference greenhouse this saving is less than 0.4% of its primary energy consumption. However, because it is a simple measure, it can still be advantageous.  159  Results In the second place, the energy saving of the insulation of transport pipes was studied. Six pipe typeswere distinguished with respect to diameter and function inthe heating system. The computations show a large difference in the effect of insulation between theoneandtheotherpipe.For thepipewiththehighestmean temperature (the main supply pipe), insulation yields an energy saving of 14GJ per meter pipe insulated per year. Insulating the gathering pipe (see Fig. 4.3 for the terminology) yields 3.9 GJnT'year"1. Insulating the transport section of the supply sideof the lower and upper heating circuit saves4.5 and 1.8 MJm"'year"1. respectively. The energy savings of insulation of thereturn transport pipesyields about half the savings achieved at their supply side. Thethird energysavingmeasure intheboilerhouseisthechangingoftheconnection of the expansion vessel if it is connected to a section in the heating system where a high temperature predominates (the main supply pipe) to a part of the heating system with relatively low water temperatures (the gathering pipe). The computations on this subject show that the savings depend to a large extent on whether the greenhouse is equipped with a heat storage tank. For a greenhouse withoutastoragetank,thesavingsare9GJyear"1,whereas thesavingsfor thereference greenhouse,havingaheat storage tank of 80m3canbe upto20 GJyear'1. Theseconditemofenergy savingmeasures involvesthedecrement ofenergylosses from the greenhouse cover. The studied measures involved the decrement of leakagethrough windows,the application of athermal screen andthe application of alternative cladding materials (coated glasspanes and double glazing). Theprevention ofunnecessary leakagethroughwindowsappearedtodecreasethe heatdemand byonly 1.6%.Thisfigure wasachievedbycomputingthe difference withrespecttoprimary energyconsumption betweenthereference greenhouseand anequal greenhouse except for 20%ofthewindowsthatremain 1 cmopenwhen they were meant to be closed. The application of athermal screen, which wasclosed during thenight whenthe outsidetemperature droppedbeneath 8°C,yields anenergy savingof 23%.However,becausethescreenconstructiondecreasesthetransparency ofthegreenhouse, the yearly photosynthesis appears to become 4% less. The specific energy consumption wascomputed to combine these effects in asinglefigure.The specific energy consumption isdefined astheyearly primary energy consumption perunit of yearly photosynthesis. For a thermal screen, the specific energy consumption decreases with 20% compared to the reference greenhouse (without a screen). Withrespecttocoatedcladdingmaterials,thecurrently availabletin-oxidecoating (HORTIPLUS)and three options for the application of an experimental polymer coating were studied. The application of atin-oxide coatingyields adecrement ofprimary energy consumption of 18%. Ontheother hand, due to the important impact ofthe coating 160  Evaluationofenergysaving techniques on transmissivity, the yearly photosynthesis decreases by 8%. Thus,the specific energyconsumption decreasesbyonly 10%.However,withexperiments onsmall glass samples, Out & Breuer (1995) reported that the negative effect of the tinoxidecoatingontransparency canbealmost cancelled outbybringing apolymer coatingontothetin-oxide coating.This leadsto aspecific energy savingequalto the decrement of primary energy consumption (which is 18%). Out & Breuer also suggested applying the polymer coating onto the glass panes of double glass greenhouse cladding. This gives a double glass pane a transparency equal to that of a single glass pane. Thus, thedecrement of specific energy consumption bytheapplication of apolymer-coated double glasscover,becomes equal to the decrement of primary energy consumption for an ordinary double glasscover.Forordinary doubleglassthedecrement ofprimary energyconsumption appears to be 31%. Withoutthepolymer coatingtheyearly photosynthesis dropsto 84%ofthereference greenhouse. Thus, for ordinary double glass a large amount of the benefits ofenergysavingarelostwhenitseffect onspecific energyconsumption isjudged. The savings of an ordinary double glass cover are then limited to20%. The ultimate suggestion with respect to primary energy saving, as posed byOut & Breuer is to make a double glass cover consisting of glass panes coated with boththetin-oxideandthepolymer coating.This claddingmaterial hasatransparency comparable to that of ordinary double glass but achieves an energy saving of48%.After combiningtheenergysavingeffect andthedecrement ofproduction the double-coated double glass pane yields a decrement of specific energy consumption of39%. Aninteresting aspectofthedecrement oftheoverallheat exchangecoefficient of thegreenhouse cover isthatthe(absolute andrelative) portion of energy demand relatedtodehumidification increases astheinsulation ofthecoverimproves.This effect originates from the fact that the temperature of the inner side ofthecover increases asitsheat loss atthe outsidebecomes less.Whenthe mean inner cover surface temperature increases,thecondensation of moisture againstthecoverdecreases. Thuswindows have to be opened more frequently to carry off moisture. When athermal screen isapplied, the absolute portion ofthe energy demand for dehumidification increases only slightly. This isbecause, by slightly openingthe screen condensation against the cover is still possible. For the coated and double glass cladding materials condensation is severely diminished, resulting in a growth of the portion of energy demand related to dehumidification ranging from 20% (tin-oxide coated glass) to 40% (doublecoated double glass) of the specific energy consumption.  161  Results Thethird item of energy saving measures wastheapplication of energy conservingheating devices.Withrespect tothisitem acondenser, aheatstoragetankand a combined heat and power engine were studied. Thecondenser wasappliedintwoconfiguration alternatives.Inthefirst configuration(termed thereference configuration) thecondenserwasattachedtotheupper heating circuit. The upper heating circuit wasalsoapplied asasecondary heating circuit,meaningthatduringperiodswithahighheatdemand,hotwaterwasadded totheupperheatingcircuit.Thiswayofoperatingtheupperheatingcircuit results in a somewhat decreased condenser efficiency, but it avoids the necessity for an additional heating circuit. In the reference configuration the condenser decreases the primary energy consumption of the reference greenhouse by 7% compared to a greenhouse without a condenser. The mean condenser efficiency is 0.77. The results show that the negative impact of the fact that, during cold periods hot water is added to the upper heating circuit, is not of great importance. Inthealternative configuration, thecondenser could beconnected toboththeupperandlowerheatingcircuit.Thisconfiguration preventstheheatingpowerofthe condenser being dissipated at the upper heating system during periods when the temperature ofthelowerheatingsystem isgovernedbyaminimum pipetemperature. In the alternative configuration the condenser saves 9% compared to the primary energy consumption of a greenhouse without a condenser. This higher saving is achieved despite the fact that the mean efficiency of the device drops from0.77to0.74. Thisseeming inconsistency isexplained bythe fact that inthe alternative configuration, during periods when a minimum pipe dominates the lower heatingcircuit, at leastsome heatisrecovered from theexhaust gases.The condenser in the reference configuration gathers more heat during those periods butthe dissipation of that heat in the upper heating circuit does not decrease the heat demand at the mixing valve of the lower heating circuit. Thus, if a greenhouse applies a minimum pipe temperature it will be favourable to creating the possibility of connecting the condenser to the heating circuit on which (during some periods) a minimum pipe temperature holds. The computations on the effects of a heat storage tank show that, depending on theC0 2 supply strategy,eitherprimary energy savings ortheincrement ofyearly photosynthesis dominates theeffect ofthe device.Energy issaved ifC0 2 issupplied irrespective oftheheat demand. If the C0 2 supply strategy avoidsheat surpluses having to be carried off by extra ventilation (termed the reference supply strategy),theapplicationofastoragetankinducesanincreasedC0 2 supply,which enhances photosynthesis. To combine both effects, like in previous subjects of study, the energy saving effect is expressed by the relation between the heat storagedimensionandspecific energyconsumption.After combination, itappears that in general, for a heat storage tank smaller than 70 m3 and for a particular 162  Evaluationofenergysaving techniques supply rate, the supply strategy irrespective of the heat demand requires less primary energy per unit of yearly photosynthesis than the reference supply strategy. Moreover, if C0 2 is supplied by combusting 50 m3 of natural gas per hectare per hour the specific energy consumption is lower than for the 25m3ha' 'hr'1 supply rate and the 75 m3ha"'hr"1 supply rate. However, the lowest specific energy consumptionswerecalculated for thereference supply strategy atarateof 75 m3ha'1hr"1, combined with a heat storage tank larger than 80m3ha"'. As far as the C0 2 supply strategy irrespective of the heat demand is concerned, themaximal decrement of specific energy consumption appears tobe 15%,holding for the highest supply strategy. For the reference supply strategy (avoiding surpluses havingtobecarried off) themaximal specific energysavingofthestorage tank is larger, namely 22%. The larger effect must be attributed to the high value of the specific energy consumption for this supply strategy if there is no storage facility. Providingtheapplication ofthereference C0 2 supplystrategy,theeffect ofaheat storagetankonagreenhousewithcombined heatandpowerthatproduces electricityfor itsartificial illumination affects boththeprimary energy consumption and theyearlyphotosynthesis.Theenergy savingeffect isduetothefactthattheCHP engine runs irrespective of theheatdemand. Theproduction increment isaresult oftheincreased C0 2 supplybecausethestoragetankcanalsobeusedtostoresurpluses form theboiler when producing C0 2 . For a greenhouse about equal tothe reference greenhouseexceptfortheillumination andtheclimatecontrollersettings inNovemberandDecember, themaximal decrement ofspecific energyconsumption is 24% compared to the situation without a storage tank. The third topic ofthe study on energy-saving heating devices concerned the application ofaCHPenginethatproduces electricity for thepublic grid.Inthiscase energysavingsareachievedbecauseelectricityproductionwithahighoverallconversion efficiency atthegreenhouse sitereplaces electricity production atalower conversion efficiency elsewhere.Taking account of energy savingsduetodiminished primary energy consumption at public power plants, the reference greenhouse appear to be able to achieve energy savings of up to 32%, holding for a CHP enginewith athermal power of 100W^per m2 greenhouse (and an electric power of 63Welm"2). If the exhaust gases of the device can be cleaned to such an extent that they are suitable for C0 2 supply, a comparable saving is achieved for an engine havinga thermal power of only 40W^m"2.  163  Conclusions anddiscussion 7. CONCLUSIONS AND DISCUSSION Under anofficial agreement withthe government - theMJA - horticulture inthe Netherlands has set itselfthetask of halving itsprimary energy consumption per unit of production by the end of the millennium, compared to itsvalue in 1980. Thequantitythatdescribestheactualprimary energy consumptionperunitofproduction asapercentagetothatholding for 1980data isreferred tobytheENSEC (Economically Normalized Specific Energy Consumption), defined as a formula inEqn. 2.1. Thus,thetarget ofthe MJAisto achieve anENSEC=50bytheend of the century. In the early 1980sthe ENSEC decreased rapidly, reaching 60 in 1985,but then increased again to about 68. By the end of 1993 the ENSEC was 66. When the tendencies with respect to primary energy consumption and production value of the last five years are extrapolated toward theyear 2000,the ENSEC at theend ofthecentury isabove 70.Thus,toreach theobjective oftheMJA,the tendency of the last years has to change drastically. To achieve this,either production (the denominator of Eqn. 2.1) should increase or the primary energy consumption (the nominator) should decrease. However, with respect to the governmental objective to decrease the level of absolute C0 2 production, as cited in theMJA, adecrement of the nominator ismuch more favourable. This isbecause iftheENSEC is decreased by enhancement ofproductiontheabsoluteleveloftheprimary energy consumption willseverely violatethe general governmental objective for thedecrement ofC02-exhaust.Therefore, the measures proposed intheMJA for the decrement oftheENSEC opt for adecrement in primary energy consumption. In this study, the perspectives of nine of these measures are analyzed. The evaluation of the impact oftheproposed measures in full-scale greenhouses isdifficult because itisveryhard toeliminate allother factors thanthesubject of survey. Moreover, full-scale experiments are expensive because the evaluations should span at least ayear and,due tothe largenumber of factors that determine energy-saving effects, a large number of experiments is required. Therefore the application of acomputer model capable of computing theeffects ofenergy conserving measures as a function of relevant parameters is to be preferred to fullscale measurements. In order to be able to create enough, and physically interpretable parameters, a deterministic simulation modelhasbeenbuiltbyassembling agreenhouse climate controller withagreenhouse climate simulation model andamodel that describes thegreenhouseheatingsystem devices.Themodel concerningtheheatingsystem devices comprised a description of the heating circuit, the boiler, the condenser, theexpansionvessel,combinedheatandpowerandashort-term heatstorage faci165  Conclusions anddiscussion lity.Allsub-models for theheating system were developed for thepresent study. Themodel describing thegreenhouse climate wasbased onthestate-of-the-art as presented in the literature. Prior to the application of models related to the computations of effects that can be expected from energy-saving measures, their results must first be shown to have a satisfying resemblance with reality. From thesub-models describingtheheatingsystem,theheatingcircuit simulation and thesub-model for theheat storage facility werevalidated with measurements carried out on a research facility at IMAG-DLO. Both sub-models appeared to simulate the physical behaviour of these heating system components very well. The sub-models for the boiler and the expansion vessel were not compared with measurements but with aggregated results presented in the literature. These comparisons showed large differences between modelling results and the results reported in literature. However, because it is reasonable to have considerable doubts about the results presented in the literature, the developed models were judged to be applicable with respect to the present work. The assembled model, when compared to detailed measurements carried out on asemi-practical greenhouse(aresearch facility atIMAG-DLO) showedagoodresemblance. Compared tolong-term measurements onthesamefacility, themodel described the yearly energy consumption with an accuracy of2%. When simulation models are to be applied in configurations that differ from the situation(s) in which it is validated, there should be no parameters that lack a physical interpretation. Moreover, such models should have not too many parameters that are difficult to measure or estimate. Both conditions were satisfied with the present model. Only a few parameters on mechanisms that cannot be readily measured (the impact of attachments ontheoverall heat exchange coefficient of heatingpipes,the discretization of the velocity profile in a storage tank, canopyevaporationandtheheatexchangethroughthethermal screen)weredetermined by iteration of model results with measurements. To analyze the energy-saving options with the model developed a greenhouse of 1 hectare producing tomatoes in the Netherlands was taken as a reference. Of course, this reference greenhouse is only one example from the wide variety of greenhousesthatcanbefound. Ifadifferent reference situationwaschosen,which canbe found easily,evenamong greenhouses growingtomatoes, many oftheresultspresented inthiswork would change.Moreover, themodel assumes thatthe heatingsystemiswellengineered. Inpractice,aheatingsystem displaysnumerous shortcomings. Here onecanthink ofashortcut between themain supplypipeand the gathering pipe that prevents the storage tank being cooled down tothereturn watertemperature oftheheatingcircuit.Another shortcoming frequently encountered isthecouplingofthestoragetanktotheheatingsystembypipesthatarenot 166  Conclusions anddiscussion wide enough. This severely limits the heating power of the tank. However, the computations on the reference greenhouse give a good impression ofthetendencies oftheenergy savingmeasures.The studiedtopicswereselected fromthe measures proposed inthe MJA and were arranged in three items. The first item comprised relatively simple improvements intheboiler house, involvingtheincrement of insulationthicknessoftheboiler,theinsulation oftransportpipesandthereplacement oftheplaceofconnection oftheexpansionvessel. The computations show that the energy savings achieved by these measures are small.Nevertheless,sincetheproposed measures areeasy,andtherefore relatively cheap to carry out, they can still be advantageous. The second item of energy saving measures studied with the simulation model concerned the decrement of energy losses from the greenhouse cover by the decrement of leakagethroughwindows,the application of athermal screen andthe application of alternative cladding materials (coated glass panes and double glazing). Under the circumstances created to study the effect of theprevention of leakage through windows, the decrement of heat demand was small (1.6%). The other measures showenergy savingsrangingfrom 18%(atin-oxidecoating)upto47% (an option using double glasswhere each glass iscoated with atin-oxide coating and aparticular polymer coating). However, the thermal screen and most of the alternativecladdingmaterialsresultinadecreasedtransparency ofthegreenhouse. Thisresultsinadecrement ofphotosynthesis.Tocombinetheenergysaving effect withthe lossofproduction, the qualities ofthethermal screen andthealternative cover materials are judged according to their impact on the decrement of the specific energy consumption. The specific energy consumption is defined as the yearly amount ofprimary energyrequiredperunitofyearlyphotosynthesis.With respect to specific energy consumption, the achieved savings range from 10%(a tin-oxide coated cover) to 39%(double coated double glass). An interesting aspect of increased insulation properties of the greenhouse cover is the increase of the energy demand of the greenhouse related to dehumidification.Thiseffect wasexplained bythedecreasingcondensation againsttheinner side ofthecover asthecover hasahigher thermal resistance. Becausethegreenhouseclimate controller doesnotallowtherelative humidity inthe greenhouseto exceed 85%RH,adecreased condensation iscompensated for byincreased ventilation.Thus,part ofthebenefits ofthediminished heat loss from thecover islost by extra ventilation. Theabsoluteamount ofenergy associated withdehumidification byopeningwindowsis240MJm"2year'' for anordinary cladded greenhouse, 320MJm"2year'' for agreenhousewithHORTIPLUSand 380MJm'2year"' for agreenhouse withdouble glass. For the cover with the lowest heat loss (double-coated double glass) the 167  Conclusions anddiscussion energy demand associated with dehumidification even becomes 450MJm^year"1 (40% of itprimary energy consumption). The large portions of energy associated with dehumidification stress the importanceofthedescription ofthevapourhousehold inagreenhousebythesimulation model. Moreover, the fact that decreased condensation is compensated by extra ventilation means that savings are (highly) over-estimated if computed with the fraction that theheat flux through the insulating covering material has decreased compared to ordinary glass. Judgement ofenergysavingproperties bymeansoftheeffects onspecific energy consumption rates primary energy saving equivalent to increment of production. This agreeswiththedefinition oftheENSEC. However, withrespecttopractical horticulture thebusiness economics effect of a decrement of the specific energy consumption by enhancing production is much larger (4 to 5 times) than if the same decrement of specific energy consumption is achieved by energy saving (providing that the costs related to the decrement are equal). This is due to the fact that the nominator affects the costs, whereas the denominator affects the benefits of production. The third item of energy saving measures analyzed in this study concerned the application of acondenser, ashort-term heat storage facility andacombined heat andpower engine.Itwasshownthatitisadvantageoustobeableto feed thecondenser withreturn water from bothheating circuits rather thanwith aconnection to the low temperature heating circuit alone. Theenergy-saving effects oftheheatstoragetankonagreenhousewithoutaCHP engine was shown to depend strongly on the C0 2 supply strategy. For a greenhouse that supplies C0 2 irrespective of the heat demand, a storage tank can decrease theprimary energy consumption by upto 12%.If thesupply strategy preventsheat surpluses havingtobecarried off byextraventilation, thestorage tank does not saveprimary energy, but rather enhances production. For this case, the model shows that the yearly photosynthesis can be increased by up to25%. The combination of both the effects by means of the computation of the specific energyconsumption showsthatthedecrement ofspecific energyconsumption can beupto22%.For small heat storage tanksthesupply strategy irrespective ofthe heatdemandyieldedalowerspecific energy consumptionthanthesupply strategy that prevents heat surpluses having to becarried off. Indeed, this C0 2 strategy is widely applied inpresent-day horticulture. Inthiscontext,itmust berecalled that thebusinesseconomicseffect ofthedecrement ofspecific energy consumptionby anincrement inproduction islarger thantheeffect ofthesamedecrement ofspecific energy consumption by primary energy saving. If a heat storage tank is applied to a greenhouse using artificial illumination powered by an on-site CHP engine, providing the storage tank can be used by both the CHPengine andtheboiler, themajor benefits arerelated to C0 2 supply. 168  Conclusions anddiscussion A large storage tank (80 m3ha"1) gives a 7% decrement of primary energy consumption butthe extra production dueto increased COz supply (providing a C0 2 supply strategy that prevents extra ventilation is used) appears to be 18%.The resulting decrement of primary energy consumption can be up to20%. If acombined heat and power engine isused for theproduction of electricity for the public grid, energy savings can only be noticed when the decreased primary energy consumption at public power plants is subtracted from the significantly increased energy demand atthegreenhouse site.Indoing so,thereference greenhouse appears to be able to achieve energy savings of up to 32%,holding for a CHPengine with athermal power of 100W,,,per m2 greenhouse (and anelectric power of 63 Wdm"2). If exhaust gases of the device can be cleaned to such an extent that they are suitable for C0 2 supply, acomparable saving isachieved for an engine having a thermal power of only 40W^m"2. Oneaspectthathasnotbeentaken intoconsideration inthestudyonCHP for the public grid is the fact that the economic value of the electricity produced is not constant.Duringpeakdemandsofelectricity,thecontributionofCHPengines(not necessarily inhorticulture) can mean that largepublic powerplantswill nothave tobeswitched on forjust short times.This means that,because ofthehighvalue ofelectricity,duringperiods ofhighpublicelectricity demand, itwillbeadvantageous to assign a higher priority to CHP than to C0 2 . Inclusion of this control strategy will leadeithertoadecreased energy saving(when thereject heat cannot bestored orapplied inthegreenhouse) or adecrement ofC0 2 supply (in casethe CHPengine prevents the boiler to produce C0 2 ). Thus,this strategy will lead to some increase of specific energy consumption. However, from a business economics point of view such a strategy can bevery advantageous. With respect to the energy savings figures resulting from an application of CHP to serve the public grid, it must be mentioned that by expressing the savings as in Section 6.3.4.3, all benefits of electricity production with CHP engines are attributed to horticulture. From a wider perspective (national scale) when comparingtheprimary energy consumption ofpublicpowerplantsproducing electricityandhorticultural boilersproducingheatwiththeCHPalternative,theabsolute savings, of course, are the same but the percentages become less. Finally, it must be concluded that the simulation model developed has proved to be isauseful tool tojudge thepotentials ofparticular energy savingmeasures in a horticultural context.  169  References  REFERENCES  ALDRICH, R.A. and J.R. Sharp, 1989, The IER vertical south roof greenhouse. In: Energy saving in Protected Cultivation, ed. B.J. Bailey, Acta Horticulturae 245, Bedford. 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Acta Horticulturae 268:71-80 GOUDRIAAN,J., 1977,Cropmicrometeorology: asimulationstudy.Simulation Monographs. Pudoc, Wageningen GOUDRIAAN, J., 1986, A simple andfast numerical methodfor the computation of dailytotalsofcropphotosynthesis.Agriculturalandforestmeteorology, 38:249-254 GOUDRIAAN, J., 1988,Thebare bonesof leaf-angledistributionin radiationmodels for canopyphotosynthesis and energy exchange. Agricultural and forest meteorology, 43:155-169 HAM, P.J., 1984, Mollier-h/x-diagrammenvoor vochtige lucht, geconstrueerd door middelvan de computer.Klimaatbeheersing 13(1984)6 Handbook of chemisry and physics, Editor: R.C. Weast, 49th edition, The chemical rubber co., 1968 171  References  Handboek Verwarming Glastuinbouw, 1995, Editors: J.B. Verveer and CD. Becque, Nutsbedrijf Westland HASHIMOTO, Y., G.P.A. Bot, W. Day, H.J. Tantau and H. Nonami, 1993, Thecomputerized Greenhouse, Academic Press, San Diego HENTEN, E.J. van and J. Bontsema, 1991, Optimal control of greenhouse climate. Proceedings of the IFAC/ISHS Workshop, Matsuyama, Japan. 27-32 HENTEN, E.J. van, 1995, Greenhouse climate control, an optimal approach, Ph.D. Dissertation, Agricultural University, Wageningen, 327 pp. HOFSTEDE, G.J., 1992, Modesty in modelling: on the applicability of interactive planning systems with a case study in pot plant cultivation. Diss. Wageningen Agricultural University, Wageningen, The Netherlands HOUTER, G. 1989,Simulatie van het C02-verbruik in de glastuinbouw(modelbeschrijving). Proefstation voor Tuinbouw on de Glas, Naaldwijk HOUTER,G. 1991,ECP-model: Simulatiemodelvoorenergieverbruik, C02-verbruiken kg-produktieindeglastuinbouw (Eindverslag).Proefstation voor Tuinbouw on de Glas, Naaldwijk JOLLIET, O. and B.J. Bailey, 1991. The effect of climate on tomato transpirationin greenhouses: measurements and model comparison. Agricultural and Forest Meteorology 1991,58:43:62 JONG, T. de, 1985.Metingenaan en simulatie vanhetkasklimaat.M.Sc. Dissertation, Agricultural University, Wageningen JONG, T. de, 1991. Natural ventilation of large multispan greenhouses. Ph.D. Dissertation, Agricultural University, Wageningen LJUNG, L., 1987,System identification:theoryfor the user. Prentice-Hall, New Jersy, 519 pp. KLEINBACH, E.M., W.A. Beckman and S.A. Klein, 1993,Performancestudy ofonedimensionalmodelsfor stratiefiedthermalstoragetanks.SolarEnergy, 50(1993)2, pp. 155-166 KLIMSTRA, J., 1991. De energiehuishouding van warmte/kracht-installaties2. Gas, 4(1991), pp. 166-171 Kwantitatieveinformatievoordeglastuinbouw 1992-1993,Groenten, Snijbloemen,Potplanten, 1992, Informatie en Kennis Centrum Akker- en Tuinbouw, Afdeling Bloemisterij/Afdeling Glasgroente en Bestuiving, Aalsmeer/Naaldwijk. MAVROS, P., V.Belessiotis and D. Harambopoulos, 1994. Stratified energy storage vessels:characterization ofperformance andmodelingof mixing behaviour.Solar Energy, 52(1995)4, pp. 327-336 Meerjarenafspraak tussen de Nederlandse glastuinbouwsector en de Staat vertegenwoordigddoorde MinistersvanEconomischeZakenenLandbouw, Natuurbeheer en Visserij overde verbetering van de energie-efficientie,1992, Landbouwschap, Den Haag MEIJNDERT, J., 1983,Juiste keuze maken bij toepassingrookgascondensor.Vakblad voor de bloemisterij 38(1983)3,pp. 72-75.  172  References  MIGUEL, A.F., N.J. van de Braak and G.P.A Bot, 1995,Massflow throughmaterials with pores and openings: H-natural convection, submitted for publication in International Journal of Heat and Mass Transfer. MONSI,M.and Saeki,T., 1953,UberdenLichtfaktorindenPflanzengesellschaften und seine Bedeutungfur dieStoffproduktion.Japanese Journal on Botany, 14:22-52 MONTEITH, J.L., 1961, An emperical methodfor estimating long wave radiation exchanges in the Britsh Isles. Quarterly Journal of the Royal Meteorological Society, 87, 171 MONTEITH, J.L., 1973,Principlesof environmentalphysics. Edward Arnold, London, 241 pp. MORRIS, C.W. and Lawrence, J.H., 1971, The anisotropy of clear sky diffuse solar radiation. Transactions of the ASHRAE 77 (2): 136-142 MUIJZENBERG, E.W.B. van den, 1980, A history of greenhouses. Institute of Agricultural Engineering (IMAG-DLO), Wageningen, 435 pp. MYNENI,R.B.,J.RossandAsrar,G.,A reviewofthetheoryofphoton transportinleaf canopies, Agricultural and Forest Meteorology, 45(1989)1-153 Nationaal milieubeleidsplan-plus, (in Dutch), SDU, 's-Gravenhage, 1989 NAWROCKI,K.R. andN.J.A.van derVelden, 1991, Gebruiksrendementenaardgasgestookteketelsindeglastuinbouw; gissenismissen,metenis(z)weten. IMAG-DLO, Nota 91-55, 81 pp. NovemEnergiegids,Van Haalen & Partners, Sittard, 1994 OUT,P.G., andJ.J.G. Breuer, 1995,Effectvangecoatglasopdelichttransmissie enhet energieverbruikvan tuinbouwkassen,IMAG-DLO, Wageningen, rapport 95-1 OVERSLOOT, H.P., 1992, Optimale integratie van WK-systemen in bestaande verwarmingssystemen met warmtebuffersin de glastuinbouw.TNO-rapport B-921048, Delft, PALM, W.J., 1986, Controlsystemsengineering.Wiley, New York, 695 pp. PITS, D.R. and L.E. Sissom, 1986, Heat transfer. Schaum, Singapore, 325 pp. Polytechnischzakboekje, Editors: M.R. Creemers e.a.,PBNA. Arnhem, 1987 RIJSDIJK,A., 1993.Minimumbuisterdiscussie.Vakdeel glasgroente,Groente & Fruit, 3(1993)45, pag 24-25 SCHINKEL, W.M.M., 1980, Natural convection in inclined air-filledenclosures,Phd Thesis TUD, Delft, 342 pp. SELLERS, W.D., 1965,Physical Climatology.University of Chicago Press. SEGINER, I., A. Angel, S. Gal and D Kantz, 1986, Optimal C02-enrichment strategy for greenhouses. A simulationstudy. Journal ofAgricultural Engineering Research, 34:285-304. SEGINER, I. and A. Sher, 1993, Optimal greenhouse temperature trajectoriesfor a multi-state-variabletomato model. In The Computerized Greenhouse, Academic Press, New York, 340 pp. SLUIS, B.J. van der, K.R.Nawrocki andN.J.A. van der Velden, 1992, Dekkingsgraden van restwarmtein deglastuinbouw. Landbouw-Economisch Instituut, Den Haag, 68 pp.  173  References  SPARROW,E.M.and R.D.Cess, 1970,Radiationheattransfer. Brooks/Cole publishing Co, Belmont, California. SPITTERS, C.J.T., H. van Keulen and D.W.G. van Kralingen, 1989, A simple and universal crop growth simulator: SUCROS87. In: R. Rabbinge, S.A. Ward and H.H. van Laar (eds.). Simulation and system management in crop production. PUDOC, Wageningen, pp 147-181 SPRENGER, E. and W Honmann, 1983, Taschenbuchfur Heizung undKlimatechnik Oldenburg, Miinchen. STANGHELLINI, C , 1987, Transpiration of greenhouse crops, an aid to climate management.Ph.D. Dissertation, Agricultural University, Wageningen: 150pp. SWINBANK, W.C., 1963.Long wave radiation from clearskies. Quarterly Journal of the Royal Meteorological Society, 89, 339 TAKAKURA, T. 1992.Climateundercover.Kluwer Academic Publishers, Dordrecht, 155pp. UDINK TEN CATE, A.J., 1983. Modeling and (adaptive) control of greenhouse climates.Ph.D. Dissertation, Agricultural University, Wageningen: 159pp. VELDEN,N.J.A. van der and B.J. van der Sluis, 1993,Energieindeglastuinbouwvan nederlandin 1991;ontwikkelingenindesectorenopdebedrijven.LEI-DLO,Den Haag, 85 pp. VELDEN, N.J.A. van der, B.J. van der Sluis and A.P. Verhaeg, 1995, Energie in de glastuinbouw van nederland;ontwikkelingen in de sector en op de bedrijvent/m 1993. LEI-DLO, Den Haag, 76 pp. VERHOEVEN, A.T.M., F.L.K. Kempkes and N.J.A. van der Velden, 1995,Warmte/ kracht-installatiesin de glastuinbuow; gebruiksrendementenen dekkingsgraden. LEI-DLO, Den Haag,76 pp. VERMEULEN P., 1987,Kosten en baten C02 doserenin de zomer:C02 doserenmet warmteopslagisrendabel, Vakblad voor de bloemisterij (1987)4, p. 40-43. VERMEULEN,P.andH.vandeBeek, 1992,BeslissingsmodelvoorC02 indeglastuinbouw; investeringsselectie& doseertaktiek; aanvullend C02 doseren en warmteopslag; kwantitatieveinformatie.PTG-verslag nr 14,Naaldwijk, 88 pp. Vademecumvoor de glastuinbouw 1978, 1978, Landbouw economisch instituut, Den Haag. YOO H. and E. Pak, 1993, Theoretical model of the chargingprocess for stratified thermalstoragetanks. Solar Energy, 51(1993)6 pp. 513-519  174  Convective heat exchange APPENDICES APPENDIX A: CONVECTIVE HEAT EXCHANGE  In his thesis, Balemans (1989) presented a thorough review of the literature on convectiveheatexchange.Therefore, thisappendixisbasedontheresultspresented in his work. Typically, convective heat exchange processes in agreenhouse are governed by free convection. Only the convective heat exchange at the outside of the greenhouse cover can be considered tobe forced by wind speed. Thus, except for the heat lossesat thecover, theNusselt number describing the exchange process can be defined as a function of the Raleigh number (Ra). The Raleigh number is defined by Ra = g p AT X3/(v a)  [-] (A.l)  With gthe gravitational acceleration (9.8 ms"2), p the thermal expansion coefficient(K"1),ATthetemperature difference (K),Xthecharacteristic dimension(m), v the kinematic viscosity ( m V ) and a the thermal diffusivity (mV). Taking P=l/283 K 1 , v=1.42-10"5 H I V and a=1.8-10'5mV 1 the Raleigh number appears to be Ra= 1.30-108ATX 3  [-] (A.2)  Thetemperature differences betweentheheatexchangingsurfaces rangebetween around 5 °C for the enclosing surfaces of the greenhouse envelope and up to 50 °Cfortheheatreleasefrom theheatingpipes.TheRaleighnumber characterizing the heat exchange at the enclosures of the greenhouse air (floor, screen and cover) lies inthe order of magnitude of 1-109.The Raleigh number for theheat exchangeprocess from the heating pipes lies in the order of magnitude of 1-106. For theupward heat release from ahorizontal surface in the considered order of magnitude for Ra,Balemans reports ontwoauthors,presenting the same relation for Nu as a function of Ra, namely Nu = 0.14 Ra033. Onan inclined surface, such asthe greenhouse cover, a first approximation isto multiply theRanumber intheNu-Ra relationwithafactor cos(i]/),where]i isthe angle with the horizontal. Thus the driving force, i.e. the gravitational acceleration, for which the Ra number takes account, is attenuated. Indeed, Gebhart (1971) shows that this approach yields satisfactory results. A downward heat flux (which may occur at the floor surface in the morning), holding for the considered value of Ra, is mentioned by only one author, who reports Nu=0.27Ra°25. TheNu-Ra relation for heatrelease attheheatingpipesisderived from Monteith (1973). Hementions arelation reading Nu=0.48Gr025. Tor air, this relation can be rewritten asNu=0.50Ra°25. 175  Appendices The simulation model uses a heat exchange coefficient (expressed in Wm"2K"'), which can be found from the Nusselt number by stating that a = Nu X/X  [Wm-2K-'] (A.3)  With A. the thermal conductivity of air (0.024 WnT'K"1)and Xthe characteristic dimension. Combining Eqn. A.2, Eqn. A.3 and the theoretic Nu-Ra relations the heat exchange coefficient for an upward heat flux is stated by: ccup = 1.70 (cos M/)033 AT 033  [Wm^K"1] (A.4)  Notethat thecharacteristic dimension hasdisappeared from theequation andthat for ahorizontal plate cos(y)=1.Unfortunately, the downward heat flux andthe heat exchange coefficient for the heating pipe does not omit the characteristic dimension. "down = °- 7 0 X<-°-25>AT 025  [Wm"2K-'] (A.5)  a  [Wm-2K-'] (A.6)  pi P e = I - 2 8 x ( " ° ' 2 5 ) A T ° ' 2 5  Thecharacteristic dimension of a heatingpipe issimply thediameter of the pipe, butitisquestionablewhatshouldbeused asacharacteristic dimension ofagreenhouse floor. A first approximation could be to take half the diameter of the Bernard-cells inwhichthe air circulates.Assuming theBernard-cells tocover an area with a diameter of about 6meters the characteristic dimension would be3. SubstitutingthischaracteristicdimensioninEquationA.5 makestheheatexchange coefficient for thedownward heat flux at small temperature differences comparable to the heat exchange coefficient for the reverse case.  176  Relation between massand heat transfer  APPENDIX B: RELATION BETWEEN MASS AND HEAT TRANSFER  Masstransfer toorfromobjects suspended inamovingairstream isanalogousto heattransfer by convection.Where for heat exchangetheNusselt number describestherate ofheat exchangebyH=Nu XAT/X,masstransfer canbe described byasimilar equation M= ShDAc/X,with Mthemasstransfer rateper unitsurfacearea(kgm'V), ShtheSherwood number,Dthemolecular diffusivity (mV1), Acthevapourconcentration difference (kgm"3)andXthecharacteristic dimension (m)(Monteith, 1973).Becauseoftheanalogybetweenheatandmasstransfer, the Sherwood number can be computed from Nu with the relation Sh=Nu(a/D)m, withathethermal diffusivity (mV). Thepowermequals0.25 for laminarconditionsand0.33whenthetransfer processisturbulent.Theratioa/Disalsoreferred to as the Lewis number (Le). For water vapour in air Le is 0.89. In the former section the Raleigh number for the heat exchange at the horizontal (or slightly inclinedplates)indicatedaturbulent exchangeprocess.Thusthemasstransfer rate can be defined as a function of Nu by: M =Nu (0.89)°33 D Ac/X  [kgrnV1] (B.l)  After substituting Nu by an expression of a the characteristic dimension disappears from the equation and Xappears in the denominator. M = a (0.89)°33 D/k Ac  [kginV 1 ] (B.2)  Equation B.2 relates the mass transfer rate to a concentration difference, but the simulation model defines the humidity as a vapour pressure, expressed in Pa (Nm"2). Therefore aconversion from vapourpressure difference to concentration difference mustbeperformed, whichcanberealizedbyapplicationofthegaslaw. Ac= ^ { J  -f2 }  [kgm"3](B.3)  withMthemolecular weight (18kgkmor1 for water vapour), Rtheuniversal gas constant(8314Jkmor'K."1),PjandP2thevapourpressuresofthemassexchanging entities(Nm-2) andT, and T2theirtemperatures (K).Consideringthatthetemperature differences will not be very large, a mean temperature of 287 K for both T, andT2canbeusedtomaketheconcentration difference dependentonavapour pressure difference only. At a temperature of 287 K and with D=2.2-10"3 and A.=2.5-10"2 and after combination of Eqn. B.3 and B.2 the mass transfer rate is described as a function of vapour pressure difference and related to the heat transfer coefficient by: M = a 6.4-10"9AP  [kgrnV'] (B.4)  177  Appendices  APPENDIX C: TRANSMISSIVITYOF A GREENHOUSE COVERING STRUCTURE  Short-wave solar radiation which encounters a greenhouse is either reflected, transmitted or absorbed by the covering structure. For direct radiation thetransmitted(andreflected) fraction dependsstrongly ontheangleofincidencebetween the ray of incoming radiation and the intercepting glass panes. Diffuse radiation comes from all directions in the hemisphere. The intensity of diffuse radiation from aspecified solid angle in the hemisphere can be defined by a distribution function. Intheliteratureseveral ofthesefunctions arementioned (Coulson,1975; MorrisandLawrence, 1971).Mostofthesefunctions define theintensityirrespectiveoftheactual solar position.Onlythecircumsolar distribution function relates the intensity of diffuse radiation to the angular distance from the sun. Irrespective oftheassumed distribution function thediffuse transmissivity canbe computedbyanumericintegration ofalargenumber ofdirecttransmissions,each giventheweightinaccordancewiththedistribution function. Thus,herethedirect transmissivity of the greenhouse for direct radiation is determined first.  C.l Direct transmissivity To compute thetransmitted radiation as afunction ofthe angle of incidence,the theory discussed inthefollowing article canbeapplied.Thispaperwasreprinted with the kind permission of the publisher.  178  Transmissivity  of a greenhouse covering  structure  J. agric. Engng Res. (1993) 56, 39-49  Determination of Direct Transmission of a Multispan Greenhouse Using Vector Algebra H. F. DE ZWART  Agricultural Research Department. Institute for Agricultural Engineering (IMAG-DLO). P.O. Box 43. NL-f>7lK> AA Wageningcn. The Netherlands  (Received N June IW2: incepted in revised form 6 February /W.f.;  The transmission of a multispan infinite greenhouse cover for direct radiation iscalculated as a function of greenhouse geometry and solar position. The calculation allows for the shading effect of the main construction elements. The solution method is based on vector algebra. It appears that the use of vectors that denote the orientation of the planes in the greenhouse cover leads to aclear, and easy to understand calculation scheme.Therefore, the method presented here can be applied to other situations as well. Due to the compact and unambiguous notation, and assuming the availability of software suitable for vector algebra, programming effort isconsiderably diminished. The results of the solution method are compared with the model of Bot. which employs similar assumptions, but based on goniometric expressions. Calculations were made for the direct transmissivity of a venlo-type greenhouse and similar results were obtained.  1. Introduction Shortwave solar radiation entering the greenhouse is an important energy source. For plant growth, solar radiation is the only source, or in cases where artificial illumination is used, the major source of PAR (Photosynthetic Active Radiation). Many modellers have developed and published schemes to calculate the transmissivity of a greenhouse, as a function of its geometry and orientation.1"9. Some of these models are concerned with light transmission of small, single span greenhouses. 2,3 Others have calculated the transmission of large multispan greenhouses, assuming an infinite cover.1,4 More recent papers present models with more general and comprehensive calculation schemes. 5-9 An important objective of many models is to determine a "figure of merit' for the transmissivity of different greenhouse constructions. The shape and orientation of covering structures were compared and improved.6"9 Because of this interest in global behaviour, the focus has changed from a detailed description of transmission to a more general approach. Another objective in building a transmission model is to get accurate information on the transmissivity of a greenhouse at each moment of the day. 2,4 This transmissivity. as a function of solar position, can be used in simulation models of canopy crop growth*or greenhouse climate models. 4 For this reason Bot4 developed an extensive model holding for an infinite greenhouse cover. However, his model requires much programming effort, owing to the large amount of extensive goniometric expressions. The determination of the shading effects of construction elements in his model is especially complicated. The model presented in this paper follows the outline of Bot's model but performs the 39 l»>-lNf>>l/T</iNiU«< » 11SlW.IXI/n  © I*'-' Silsoc Research Imcuulc  179  Appendices  40  TRANSMISSION OF A ML'LTISPAN GREENHOUSE  Notation B Ct...C,  D d £,...£, h />./: G 0 /  i  L,,L2  N, N,,N, n R,.R, R,.R2 *P  bar distance vector vector to corner points ofthe cross section of a glazingbar vector from onegutter tothe next gutter distance,m three ridge corner points height of ridge above gutter. m fractions of the light beam gutter direction vector three-dimensional light beam vector two-dimensional light beam vector (projection inthe .r<:-plane) angle of incidence,deg two-dimensional light beam vector projected in theyNx and yH2 plane respectively normal on the twodimensional light beam vector I normal on pane R, and R : respectively number of spans passed by the light beam set of twovectors describing a glass pane projection ofR, andR2inthe xz-plane respectively projection of a pane ond  RzP projection of R2 onD 'n transmissivity of the/, fraction of D '.- transmissivity of the / . fraction of D £ / , . . . £ / , three gutter corner points 0} solar elevation,deg ex-., e, fraction of thethree ridge corner point shadows with respect toD fraction of the three gutter Mi • • • M > corner point shadows with respect toD A multiplication factor between D and Rp A: multiplication factor between D and R2p V  multiplication factor between B andtheprojections of C)...C>  * roofslope.deg P reflection coefficient reflection on inner sides ofthe Pirmard R ; panes r transmission coefficient r„ r2 transmission coefficient ofa pane R, and pane R : T transmissivity of the bars inthe b l - fk> R, andR2 pane total transmissivity ofthe cover '^cover k azimuth ofthegreenhouse,deg L azimuth of thesun.deg  calculation in a much more efficient way by the use of vector algebra. Moreover, vector algebra improves the understanding of the method and the calculation of shading by construction elements is simplified. This paper treats only the direct transmission. Diffuse transmissivity can be calculated by taking the weighted average of the direct transmissivities. Distribution functions to determine the relative weight to be assigned to the direct transmissivities for the different angles of incidence can be found in the literature.4,7'10 2. Theory 2.1. A greenhouse in vector notation In general, a greenhouse cover is constructed of repeating roof elements. Due to this regularity the cover can be characterized by three parameters (see Fig. 1). Theazimuth  180  Transmissivity of a greenhouse covering structure  41  H. F. DE ZWART  Fig.I. Basic greenhouse geometry with f„ the azimuth, i/rthe roofslope and d the gutter distance  (£g) indicates the angle between the gutter of the greenhouse and the north-south direction. The roofslope(i/<) and the gutterdistance (d) determine the geometry of the roofpane. To solve the transmission problem all directional indications (greenhouse construction and incident light beams) are expressed as vectors in a coordinate system related to the greenhouse (see Fig. 2). The light beam vector, D, isdefined as: D = l cos(£s-£g)cos(o>) -sin(a))  (1)  With £,azimuth of the sun.fgazimuth of the greenhouse,esolar elevation. Due to symmetry, only light from the third quadrant of the .rv-plane needs to be  Fig. 2. Vectors in the greenhouse co-ordinate system with I, the light beam vector, <o.the solar elevation, (, and £„, the azimuth of the sun and the greenhouse respectively, h = id tan III/)  181  Appendices  42  TRANSMISSION OF A MLLTISPAN GREENHOUSE  studied. Light entering from other directions can be mirrored to the third quadrant. The two roof parts are panes in a three-dimensional space. Each of these panes (R, and R;) can be described bva set of twovectors. (2)  where h = trf tan(</<), is the height of the ridge above the gutter. The second vector of each pane is the gutter direction vector, G. The transission and reflection of a glass pane dependson the angle of incidence with the normal of the glasspanes.The normals Rj| and M:,corresponding with R, andU2 are given by: (3)  2.2. Calculationof thetransmission throughthe glass panes  Given both the normal to each plane and the incident light vector the angle of incidence (/') can be calculated using an adapted cosine rule. /abs /=arccos /absMI,IM»  MINI / where (D.M) means the scalar product of 1and M. |8| and [N mean lengths of IIandM respectively (N =V(IVN)). The adaption is the 'abs' operator, providing an angle of incidence between 0and$n. U the angle of incidence (/') is known, the reflection (p), transmission (r) and absorption coefficient (a) can be determined. The theoryof transmission and reflection of transparent surfaces is not relevant in the discussion of the vector approach to the transmission problem. Therefore only a graphical representation of p and r is presented here for glass, the most used cladding material (see Fig. 3). These graphs were determined by using the Fresnel equations (e.g.Corson and Lorraine," Jefimenko12). 2.3. Transmission of agreenhouse construction With a high solar position the direct sunlight partly passes through the roofpanes R, and R2-Thissituation isdepicted in Fig. 4.The picture isa two-dimensional projection of the greenhouse on the xz-plane. Because the previously defined vectors to determine the greenhouse construction and light incidence were calculated in an orthonormal coordinate system, the transition to the new two-dimensional orthonormal system can be performed by just leaving out the y co-ordinate of the vectors. In so doing, the second vector describing the panes R, and R2 [see Eqn (2)] disappears and the following new, two-dimensional vectors are derived.  182  ()  Transmissivity of a greenhouse covering structure  43  H. F. DE ZWART  20  40  60  80  Angleof incidence.ideg.  Fig. 3. Reflection (p) and transmission coefficient (T) of a 4mm thick glass pane, as a function of angle of incidence  The transmission pattern is repeated for every gutter-to-gutter distance. Therefore, the calculation is performed on the direct transmission entering one roof-section only. The transmission isthe sum of the light transmitted by the panes /?, and R2. Byusing Eqn (4) the anglesof incidence can be determined and a transmittance for both the panes can beascertained. Theseparation of the beam between tworidgesinto a part through /?, and a part through R2 isdetermined bythe fractionsf, and£ (see Fig. 4). A careful study of Fig.4 shows that the part of the light beam through R2 is the projection of R2 along the direction of / on D, where D is the vector pointing from one gutter to the next.  -0  (6)  RP = W  (7a)  The projection isdefined by: with A=  (N„R)  Fig. 4. Transmission and reflection on the greenhouse cover at high solar positions. R2, projection of the vector R2 on D, N, is the normal to I  (7b)  is the  183  Appendices  44  TRANSMISSION OF A MLLTISPAN GREENHOUSE  Where N, is the normal of / in thexz-plane,calculated by: sin(ai)  N, - ( sin(£,-&) cosM J  ^  (8)  Ascan be seen in Fig. 4the fraction f2 is the length of the projection of R2. marked R2p. with respect to D. f2 can be calculated by: h = R^/D  (9)  However, the signed length ratio was.in fact, already defined by the term A in Eqn (7b). When the multiplication factor for the projection of R2 on D is denoted A:, /; can be calculated bv: f2=abs(A;)  (10)  The absolute value providesf2 a positive number. The fraction /, is the fraction of light through the panes /?,. It isthe complement of f2. /.= ! - / :  (ID  For the case where the solar elevation angle (projected in the xz-pane) exceeds the roofslope. the transmission of the greenhouse cover can be expressed as: rc„«,=/iT,+/ : r 2  {A2<0}  (12)  where T,, and x2 transmission coefficients of /?, and R2 respectively [with an angle of incidence calculated by Eqn (4)] Reflections at the outer sides of the covering glass panes, marked bya grey shading in Fig. 5, are directed away from the cover. This holds for both panes /?, and R2 as long as the projected angle of incidence exceeds three times the roofslope. When the projected angle of incidence lies between i/» and three times the roofslope the reflections from R2 interact with /? t . However, the large angleof incidence with /?, results inahigh secondary reflection on that glass pane. Thus the amount of light reflected by R2, followed by transmission through Rt is negligible. Therefore, no further attention is paid to the reflections of the outer sidesof the cover at high solar positions. The next situation is when the light beam intercepts the greenhouse with an angle smaller than the roofslope. This is shown in Fig. 5. In this case, all radiation first passes  -tx  m.v+l  Fig. 5. Transmission andreflection of a light beam with an angle of incidence smaller than the roofslope  184  Transmissivity of a greenhouse covering structure  H. F. DE ZWART  45  Fig. 6. Transmission and reflection of light coming in at very low elevation angles.  through /?,. After passing through R, part is transmitted by R2. followed by passing through another pane /?,. Although R2p is now pointing in the same direction as D. the fraction of the light passing these three panes isstill represented by R2p. Therefore./, and /, can still be calculated by Eqns (10) and (11). Fig. 6shows asituation where the solar elevation hasdropped to such an angle that all light passes more than one glass pane before reaching the greenhouse floor. It will be noted from Fig. 6 that R2p has grown longer than D itself. However, the beam of light falling in between two ridgescan still be divided into twoparts.The part/, is transmitted twice bya R{ pane and once by a R2 pane.The other part (/2) is transmitted by three R, and two R2 panes. It can be shown that/. can be expressed as: /, =fractional (A2)  (13)  Where "fractional" means the fraction part of the expression in the brackets [e.g. fractional (1-23)=0-23)]./, isstill determined by Eqn (11). Both the expressions for/;, namely Eqns (10) and (13).can be combined to derive a general expression. f, =fractional [abs(A2)]  (14)  As demonstrated in Figs 5 and 6, the amount of roof sections passed by a light beam increases when the angleof incidence decreases. Itcanalso beseen that light reflected on the inner side of the panes, R2 (coloured grey) contributes to the amount of light coming into the greenhouse. A suitable indication of the number of passed glass panes is A:, as calculated by Eqn (7b).The situation of Fig. 5istypical when A2isbetween 0 and 1. Fig. 6.where the entire beam passes through the panes /?, and R2, before it splits in/, and/., istypical for the situation where 1 *sA:< 2. It appears that the situation changes with the truncated value of A2.Therefore, a new number (n) is introduced with the definition: /t=trunc(A2)  (15)  where the operator "trunc" is supposed to generate the integer part of the number A2. Given n. the transmission for the/, and/. part of the beam can be determined. ,  {A2^0}  (16)  Besides the transmitted light, some light also enters the greenhouse by reflection against the inner side of the passed R: panes (see the down-directed, grey-coloured reflection beams in Figs 5 and 6). The fraction of the outside light beam reflected inward is  185  Appendices  46  TRANSMISSION OF A MULTISPAN GREENHOUSE  expressed by: Pinward  =P2((ir* 1 ^- 1 )+/ 2 TT +1 T;)  (17)  where p2 denotes the reflection coefficient of R2 [with an angle of incidence calculated with Eqn (4)].Thefirstterm between the large brackets contributes to the attenuation of the entire beam due to the multiple passing of /?| and R2 panes. The second term expresses the extra attenuation of thef2 fraction, which passes twopanes more than the/, fraction. Now the total transmission can be determined from Icover _ f If1+ f2t(2 "*" Pinward  The calculation scheme presented issuitable as long as the projected solar elevation (the anglebetween D and /) isnot toosmall,because ngrowsto infinity asthe projected solar elevation tendsto0.However, theshadowing ofconstruction partsat lowelevation angles prohibits transmission anyway. Therefore, it is recommended that the transmission calculation should be discontinued when A2>10. 2.4. Shadowing of ridges andgutters In the previous section a theoretical greenhouse cover wasobserved,consisting of glass panes only.In practice,construction elementssupport the cover (see Fig. I). Therefore,a cross-section along thecover, with exaggerated ridgesand gutters,looks more like Fig. 7. In thefigure,six corner points (£,, £ 2 , £>and UuU2, Uy) play a role in the shadowing problem. The corner points are projected on the horizontal plane,yielding (e,, e2,e3and fti, /i 2 , ptj). These projections can becalculated with Eqn (7b),just like the calculationof A2,being the projection of R2. In the constructed situation of Fig. 7,the value of all eand fi are positive,due to thechoice of the (0,0) co-ordinate. From the picture it isobviousthat the fraction shaded bythe gutter can be expressed as /x3- fix. The width of the beam coming in between the two ridges can be determined by e3-e,. Thus, the unmasked part of the light beam can be determined simply by  (0.0)  Fig. 7. Cross-section of a greenhouse ridge-gutter system  186  (18)  Transmissivity of a greenhouse covering structure  47  H. F. DE ZWART  (0.0)  Fig. 8.Cross-section ofagreenhouse coveringpane. Bis the bar-distance vector. C,,C,. C,, andC4 arecornerpoints comparing the lengths of a set of corner point projections. In the situation shown in Fig. 7, the unmasked fraction isthe width of the beam, diminished by the width of the gutter shadow.Even a(partial) coincidence of the shadesof a ridgeand agutter can be detected easily byanalysing the lengths of the projections. 2.5. Shadowing byglazing bars The shadowing by glazing bars can be calculated by analogy with the shadowing of ridges.A cross-section of acovering pane isshown in Fig. 8.The vector L isa projection of the three-dimensional light beam vector I(Fig. 2) in the two-dimensional orthonormal plane containing the normal of a glass pane [described by Eqn (3)] and the gutter direction vector G [defined in Eqn (2)J.Given these vectors,the projection Z.,of 1 in the plane <N,)(G> is: Ll =  (GVlGl)(I)  (20)  The projection of L2 in the plane (A^XG)can be determined in an analogous way. The superscript T means the transpose of a vector (i.e. turning a column vector into a row vector, or viceversa). Once L, is determined, the relative length of the projection of the corner-points along L, on 5 with respect to B isgiven by: V  Xe{1 2 3 4 «= ( ( | ^ ) ) ' ' < > /Vu denotes the normal vector on L. From the picture it isobvious that the shade of the barspans the area enclosed by v4and v2.Thus,the unmasked fraction of the bar-distance iscalculated by 1 - (v2- v4). In general the "transmissivity" of the bars in a pane can be determined by  rb= 1 - (max{v,, v2, v3,v4}- min{v,.v2, v3, v4})  (21  >  (22)  Once rbl iscalculated for the roofpanes R, and rb2 for the panes R2,Eqn (12) becomes: Tcover=/ir,rbl +f2r2Tb2 {A,<0} (23) For low elevation angles (A 2 ^0) the transmittivity of the panes, taking account of the  187  Appendices  48  T R A N S M I S S I O N OF A M L L T I S P A N O R E E N H O l SE 1 Or  S 06  Fig. 9. Direct transmissivity of a venlo-type greenhouse presented by Bot4 (Fig. 9a) and calculatedbyvector algebra IFig. 9b). r„ denotes the transmission of the bars. rK the transmission by the glass panes, rrK the unmasked fraction of the ridge-gutter system, and T„„denotes the total transmissivity for direct radiation. The result holds for a north-south oriented greenhouse at 52" latitude on 22 March (equinox).  masking byglazing bars, isdetermined by:  'n=(r,r h ,r'(r : y n  {A : >0}  Multiplying (23)or (24) by the fraction not masked bythe ridge or gutter, yields the final direct transmissivity of the construction. 3. Results The theory above has been used to calculate the direct transmissivity of a venlo-type greenhouse. The results were compared with the results derived by Bot. The results of both models are shown in Fig. 9. The calculation of the transmission of the roof-gutter system (rrg), as calculated by Bot4 and shown in Fig. 9a, showed especially good resemblance with rrg, ascalculated with the method presented in Section 2.4.(Fig. 9b). However, there were significant differences for rb(the transmissivity of the bars) and rg (the transmissivity of the glass solely) found by Bot, and those calculated with vector algebra. The sharp decrease of rg in Fig. 9b,at about 0800hrs, marks the point where the angle of the light beam falls on the upper side of the R2panes (since A2<0) with a large angle of incidence. The reflection of this beam iscast on the neighbouring pane R,. and. after being transmitted by the R, pane, contributes to the amount of light in the greenhouse. Contrary to the neglect of these reflections in the model presented here, the model of Bot accounted for this effect. After about 1000hrs, where the solar elevation is more than twice the roofslope, the reflections on the outer side of R2 are directed away from the greenhouse (as depicted in Fig.4) and the results for rg of both the models coincide. The difference in the curves of rb are caused by a different definition of the  (24)  Transmissivity ofagreenhousecoveringstructure  H. F. DE ZWART  49  transmissiviity of bars. Bot defines rh as the unmasked fraction of the projection of one roof section. The model presented here accounts for the increased shading by bars when the light passes multiple roof sections, as is the case at low elevation angles. 4. Conclusions The use of vector algebra to determine the direct transmissivity of a greenhouse yields easy-to-use relationships. One formula [Eqn (7b)] can be applied to determine the length ratios of projections of all kinds of vectors. With Eqn (20) the light beam vector can be projected easily into any plane of the greenhouse construction. Thus the shades of all kinds of solid bodies of the construction and within the greenhouse can be studied. The results of the transmission calculation based on vector projections were compared with the results of the transmission model presented by Bot, 4 which is built on goniometric expressions. The results of both models were similar for the direct transmissivity of a venlo-type greenhouse. The theory in this paper has been presented on the basis of a venlo-type greenhouse. However, as long as ridges and gutters are parallel to one another the method can be used for other types of greenhouses, such as houses with asymmetric roofshapes as well. References Staffers, J. A. Lichtdoorlatendheid van met vlakke materialen bedekte warenhuizen. [inDutch]. Wageningen. 1MAG. ITT publ. 14. 1967,35pp. Kozai, T.; Goudriaan, J.; Kimura, M. Light transmission and photosynthesis in greenhouses. Wageningen Centre for Agricultural Publishing and Documentation (Pudoc) 1987.99pp. Thomas,R. B.The use of specularly-reflecting back wallsingreenhouses.Journal of Agricultural Engineering Research 1978,23:85-97 Bot, G. P. A. Greenhouse climate: from physical processes to a dynamic model. Ph.D. Dissertation. Agricultural University, Wageningen. 1983.240pp. Critten, D. L. A computer model to calculate the daylight integral and transmissivity of a greenhouse. Journal of Agricultural Engineering Research 1983, 28:61-76 Critten, D. L. A theoretical assessment of the transmissivity of conventional symmetric roofed multispan E-W greenhouses compared with vertical south roofed greenhouses under natural irradiance conditions.Journal of Agricultural Engineering Research 1985,32:173-183 Critten, D. L. A general analysis of light transmission in greenhouses. Journal of Aericultural Engineering Research 1986,33:289-302 Rosa, R. Solar and thermal radiation inside a multispan greenhouse. Journal of Agricultural Engineering Research 198840:285-295 Rosa, R. Solar irradiation inside a single span greenhouse. Journal of Agricultural Engineering Research 1989,43:221-229 Litlefair, P.J.The luminance distribution of an average sky.Lightingand research technics 1981. 13(4): 192-198 Corson, D. R.; Lorraine, P. Introduction to electromagnetic fields and waves Ch. 11: 361-372. San Fransisco,C. C.Freeman and Cy.San Fransisco, 1962,552pp. Jefimenko, O. O. Electricity and magnetism, Ch. 8: 233-258. New York, Appleton-CenturyCrofts. 1966,591pp.  189  Appendices The theory presented in the article was applied to compute the transmissivity of aVenlotype greenhouse with agutter distance of3.20 meter (dinthepaper) and a roof slope of 25°($ inthe paper). The cladding material was 4 mm thick and thebartobardistancewassetto 1 m.Theridgewasvery small,namely 2x2 cm, which implied that thevectors £,, E2 and E3 were (1.61 0.76)', (1.61 0.74)' and (4.79 0.74)' respectively. The gutter of a real greenhouse is usually not rectangular, but nevertheless approximated by a 6x6 cm square. Thus the corner points U„U2andU3were(3.23 0.06)', (3.170.06)' and(3.170.00)' respectively. The bars intheroof were of about the same size astheridge,which implied that C„ C2, C3and C4were (0.99 0.02)', (1.01 0.02)', (1.01 0.00)' and (0.99 0.00)' respectively. TableC.l showstheresults ofthecomputations for agreenhouse from which the gutter direction points North-South. TableC.1 Transmissivity of a greenhouse covering structure as afunction of azimuthandelevation. azimuth  islevatiori  0°  3°  5°  8°  10°  15°  20°  25°  30°  40°  60°  0°  .000 .000 .000  .151 .298 .398 .413 .414  .263 .339  .336 .384  .486 .500  .678 .674  .510 .553 .559  .532 .608  .556 .651 .717  .598 .599 .616  .735 .729 .724  .800  10° 20° 30° 40°  .069 .226 .277  .795 .788  .646 .844 .841  .783 .777  ,839 .837  50° 60°  .000 .000  .554  .256  .411 .404  70° 80°  .000 .000  .245 .241  .400 .404  .773 .770 .770  .835 .834 .834 .834  90°  .000  .245  .412  .000 .000  .295 .284 .268  .625 .623  .548 .547  .620 .618  .533  .621 .629  .562  .722 .724 .724  .650 .702 .765  .675 .683 .699 .724  .775 .777  .753 .781  .727  .779  .733  .783  .801 .809  .721 .721 .728 .737 .748 .758 .764  .772 .775  .836  C.2 Diffusive transmissivity Thesimplestdistribution function describingdiffuse radiation istheuniform overcastsky.Suchadistribution, beingoneinalldirections,holdsfor aheavyclouded day.Otherdistribution functions, suchas 'standard overcastsky' (Coulson, 1975) and 'hemispherical radiation' (Morris and Lawrence, 1971) give more weight to radiation from the zenith than to radiation coming from low elevation angles.A 'circumsolar radiation' distribution (Morris and Lawrence, 1971), representative for sunnydays,givesextraweighttothesector ofthehemisphere around thesun. Bot (1983) analyzed the effects of these distribution functions on the resulting 190  Transmissivity of agreenhousecovering structure diffuse transmissivity of the greenhouse. He found significant variations. Neverthelessthemodeldiscussedhereusesasinglediffuse transmissivity number, based onthestandard overcast sky according toCoulson (1975).Duetothesymmetry ofthegreenhousetheintegration overthehemisphere canbeperformed by: „ 'dirto®* ( 1 + 3sin(P)V4) sin(p)cos(p) dp dco  ^difT=-^TvT* 'An  J0  (1 +3sin(p))/4) sin(P)cos(P) dp  H (CD  in which Pis the elevatation and coisthe azimuth. In Eqn. C.l the term ( 1 + 3 sin(p))/4 represents the distribution function for a standard overcast sky. Obviously it rates radiation coming perpendicular to the earth's surface 3timescompared toradiation comingfromjustabovethehorizon. The integral above has been approximated by a numerical integration with steps of 10° in both azimuthal and elevational direction yielding x diff =0.79  H(C2)  191  Appendices APPENDIX D: LIGHT ABSORBTION BY A CANOPY STAND  Downward directed short-wave radiation, propagating through acanopy standon its way down, ismade extinct by absorbtion and reflection at the canopy leaves. The description ofthe resulting radiation profile wasthoroughly discussed inthe Ph.D. thesis of Goudriaan (Goudriaan, 1977). His work elaborated on the idea introduced by Monsi & Saeki, to describe the extinction of light in a canopy by an exponential curve (Monsi & Saeki, 1953). For idealized canopy stands,characterized by leaveswith an equal reflection and transmission coefficient, arranged in a horizontal or spherical leaf angle distribution, planted in a non-reflecting soil, Goudriaan derived analytic solutions to describe the profile of radiation. However, if one or more of these assumptions areviolated ananalytic solution canno longer begiven.Forthosecases anumerical procedure was presented. In greenhouses thesoil ismostly covered with areflecting sheet, and thecanopy architecture tends to aplanophile leaf angle distribution. Therefore, in this work the numerical approach along the routes posited by Goudriaan is applied. The model assumptions are stated briefly, followed by apresentation of results.  D.l Model description The basis of the model isthe concept of a canopy as a series of stratified layers. The surface covered by leaves ineach layer is supposed to be randomly distributed within the layer. Therefore, in each layer the chance that a ray of light is intercepted by a leaf is the same. For each layeraradiation balanceisconstructed, consistingofupward anddownward fluxes. The downward flux in a layer iscomputed from thedownward flux transmitted bythelayerabove,supplemented byupwardradiationwhichisreflected downward by that layer. Transmission takes place through the space which is not occupied by leaves,and through the leaf tissue.The computation of the fraction of light intercepted and redistributed by transmission and reflection takes account of the dependency of the intercepting surface on the directional characteristics of the radiation. This means that radiation entering the canopy stand on low anglesofelevation isextincted more rapidly than radiation entering from the zenith. In order to be ableto compute this elevational dependency the leaf angle distribution function hastobeknown.Azimuthal preference ofthecanopy leaves is left out of consideration. All reflections and transmission through the leaf tissue are assumed to generate isotropically distributed diffuse radiation.Thisassumption issimple,butsupposed to be realistic enough (Gutschick and Weigel, 1984), especially for light transmitted bythetissue(Myneni et.al., 1989).Thus reflection andtransmission gene192  Lightabsorbtion bya canopy stand rate diffuse fluxes, even if the radiation entering the canopy stand would havea direct component only. The last layer in the model represents the soil surface, which does not transmit short-wave radiation, but reflects part of it isotropically back into the canopy.  D.2 Results with the model Anumerical model,basedonthetheorypresented byGoudriaan wasbuiltandappliedtocomputetheabsorbtion ofshort-waveradiation inacanopystandforboth visible wavelengths (VIS) and the near infra red region (NIR). Moreover, anextinction coefficient for VIS and long-wave radiation isdetermined. All computed quantities are determined for diffuse radiation and for direct radiation in four classes of solar elevation. Thecomputations hold for acanopywithaplanophile leafangledistribution. The relative frequency of leaves having a leaf angle with the horizon in one of the nine distinguished elevation classes is displayed in Figure D.l  Relativefrequencyofleafangles 0.25  0.2 0.15H  0.2201 w—*i 0.2069  0.1822 0.1489 0.1111  0.1 0.05 H  0.0733  0.0401 0.0153 v-•• • j 0.0022  0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 leaf angle class FigureD.l Relativefrequencyof leafanglesofa canopywithaplanophileleaf angledistributionfunction innineelevation classes. For VIS, the transmission coefficient of the tissue was set to 0.10, which is an appropriate mean value for green leaves inthispart of the spectrum (Goudriaan, 1973).ForNIRthetransmission coefficient ismuch larger,namely 0.46.Theleaf reflection coefficients for VIS andNIR aresetto0.05 and0.38 respectively. The reflection coefficient of thefloorwas assumed tobe 0.25 for both VIS and 0.40 193  Appendices forNIR.Diffuse radiationwasassumedtoberepresented bytheuniform distribution function. Theabsorbtion ofradiation playsaroleinthethermal sub-model that determines the greenhouse energy budget and inthe C0 2 sub-model, where the VIS profile determinestheassimilation rate.Inbothcontextsthesametheory ontheradiation profile withinthecanopyholds,butbecausethequantitiesofinterest differ forthe two cases the required quantities are determined in two sections.  D.2.1Absorbtion of short-waveand long-waveradiationin a canopystand To compute the absorbtion ofradiation bythe canopy, the radiation absorbed by the soil surface and the upward radiation flux at the top of the canopy (being a resultant of numerous reflections within the canopy) was subtracted from the downward radiation flux towhichthecanopy was exposed.Figure D.2showsthe result of this subtraction for a diffuse radiation flux in theVIS and theNIR part ofthespectrum.BoththeeightvaluesoftheLAI forwhichthecanopyabsorbtion was computed and a smooth curve fitted through these points are displayed.  Absorbed fraction  LAIN FigureD.2 Canopyabsorbtion ofdiffuse VISandNIRfor eightvalues oftheLAI and asa smoothfittedcurve. Thesmooth curveinFigure D.2for VISisdescribed by0.95 -0.9exp(-0.85LAI) andthecurve describing the absorbtion of radiation inthenear infra red band of wavelengths reads 0.65 -0.65 exp(-0.27 LAI).  194  Light absorbtion bya canopy stand Fordirectradiationtheabsorbed fraction dependsonbothLAIandsolar elevation angle. Figure D.3 shows the computed fractions of direct radiation absorbed by the canopy and again a number of fitted curves.  Absorbed fraction  FigureD.3 Canopy absorbtion ofdirect VISandNIRfor eightvaluesofthe LAI andfor solarelevationangles ranging from 5° to 65° with steps of 10°.Through thepoints a numberof curvesarefitted. The full curves inFigure D.3 for radiation inthevisible band ofwavelengths are described by0.95 -0.9ex/?(-kVISdirLAI), withk vlSdir =0.88+2.6exp(-0.18p).The curves holding for near infra red direct radiation in Figure D.3 are described by a - b ex/>(-kNIRdir LAI), with the coefficient a= 0.67 - 0.36 exp(-0.095P), the coefficient b=0.68-0.50exp(-0.l1 (J) and kN1Rdir=0.25+0.38exp(-0.12P). For long-wave radiation canopy leaves are assumed to be black (Stanghellini, 1987). Thus the absorbtion of long-wave radiation can be computed with the theory outlined above, after setting the reflection and transmission coefficients 0, and studying the absorbtion of diffuse radiation. Figure D.4 showsthe absorbtion of long-wave radiation, both as computed points and as afittedcurve. The smooth curve is described by 1— exp(-0.94LAI). The factor 0.94 is referred to as the long-wave extinction coefficient (k,).  195  Appendices  Absorbed fraction  LAI[]  FigureD.4Absorbtionoflong-wave radiationfor eightvaluesoftheLAIandas fitted curve.  D.2.2 Radiationprofile within a canopy stand Becauseof thestrongnon-linearity ofthephotosynthesis response curve thetotal assimilation rateofacanopycannotbededucted from thetotal amount ofabsorbed radiation, but must be computed by integration of the contribution of leaves throughout the canopy stand. To compute the photosynthetic activity at arbitrary height in the canopy the local intensity of radiation to which the leaves are exposed hastobeknown. Therefore theradiation profile hastobedetermined. The intensity of radiation at each layer in the model can be stated as the sum of the computed upward anddownward radiation flux for that layer.Theresults ofthese computations for diffuse radiation are shown in Fig. D.5 for anumber of LAI's. Obviously the intensity of radiation to which the leaves at the top of the canopy areexposed exceedsthedownward diffuse flux. This isaresult ofupward reflections. For very small canopies this increment of the amount of radiation appears to be more than ten percent. The computed radiation profiles shown in Figure D.5 can be approximated quite well with exponential curves of the form I(x) = I0 a exp(-kxLAI)  [Win2] (D.l)  where I(x) denotestheintensity ofradiation atrelative canopy depthx(0<x<1), I0 denotes the radiation flux at the top of the canopy (Wm"2), a a multiplication factor taking account for the increment of radiation intensity at the top of the 196  Light absorbtion by a canopy stand  canopy due to upward reflections and k an extinction coefficient. In Figure D.6, for a canopy with a LAI=1 and a canopy with a LAI=3, the approximating exponential curves are shown as full lines, together with a number of points. The points are elements of the curves shown in Fig. D.5.  Relative intensity [Wm-2] 1.<J  "-I  , 1-  ^  0.8-  LAI = 0.5 / ^   0.6-  LAI = 1.0 hM  ^ ^ v  =  1.5 LAI = 2.0  0.4^  LAI = 3.0  LAI = 4.0  0.20-  1  1  1  .  1  1  1  0.5  r—  — i  1.5  '  1  •  1  '  2.5  1—  —'  1  '  3.5 4 4.5 cumulative LAI [-]  Figure D.5 Computed radiation intensity as afunction of the cumulative LAI, expressed as afraction of the diffuse downward radiation flux at the top of the canopy for a number of values of the actual LAI of the canopy. Relative intensity [-]  0.5  1  1.5  2  2.5  3 3.5 cumulative LAI [•]  Figure D.6 Fitted radiation profiles for diffuse radiation 197  Appendices The curves inFigure D.6 aredescribed usingEqn.D.l witha andkaccording to a=1.04+0.24exp{-2 LAI) and k=0.85-0.27exp(-0.69LAI). The radiation profiles for direct radiation donotdepend onthecanopy sizeonly, but on the solar elevation angle aswell. In figure D.7 theprofiles computed for four solar elevation angles and for two canopy sizes are shown. Relativeintensity [-]  2  2.5 3 3.5 cumulative LAI[-]  FigureD.7Computedradiationprofilesfor directradiation enteringthecanopy withan elevationangle of 5°, 15° 25°,and 35°for a canopy witha LA1=1 ( ; and a LA1=3 ( ; Just like the profiles for diffuse radiation, after determination of the parameters a and k, the curves in Fig. D.7 can be approximated with Eqn. D.l. The curves for direct depend on two variables, namely the LAI of the canopy and the solar elevation angle. FigureD.8showsthecomputedradiation intensityprofiles (thesquarepoints)and theradiation profiles approximated byanexponential function ofthetypeofEqn. D.l, holding for a canopy with a LAI=2. Obviously, the approximation is better for higher elevation angles than for the low elevation angle of 5°. For direct radiationthedependencyoftheparameteraonthecanopysizecouldbedescribed bya=1.06+0.26exp(-2LAI).Theparameter kdependedonbothcanopy sizeand solar elevation angle.After introducing three intermediate parameters, kwasdescribed byk=p+qexp(rp). Theparameters p,qandr contribute for thecanopysize effect according to p=0.76-0.87exp(-1.84LAI), q=-0.95LAI+4.83 and r=0.02LAI-0.17.  198  Light absorbtion bya canopy stand  1o  Relative intensity [-]  l.i  10.80.6-  V  •   0.40.2-  B=25° »w  ^SS^^ftSw  a )w  6=5°  6=35°  X^Srn^  .  ^^* "J^^*'  7 ^ ^ 6 =15° •  o-  ,  1  0.5  i  J  •  1  •• — i  1.5  •  •  • •  1  •  2 cumulative LAI[-]  FigureD.8 Fittedandcomputedradiationprofilesfor directradiation. The intensities of the radiation flux from direct radiation inside the canopy, as showed intheFiguresD.7andD.8,donotconsistofdirectradiationonlybut,due to scattering of the radiation, are a mixture of direct and diffuse radiation. Moreover, leaves are either sunlit, meaning that they are exposed to the full intensity of the direct flux, or are in shade, where they receive diffuse radiation only. Thus, the sunlit leaves are exposed to radiation at a much higher intensity therest ofthe leaves. Because thephotosynthetic response isstrongly non-linear (see Appendix I), the pure direct radiation flux at the sunlit leaves must be distinguished from the total radiation intensity in the canopy. Tocomputethepuredirectradiation intensity,themodeldescribed inSectionD.1 wasapplied,after settingthetransmission andreflection coefficients ofthecanopy leaves0.This yielded aradiation profile showed inFigure D.9.Again,the figure showspointscomputed withthemodel andcurvesdescribed byEqn.D.l. For all curvesinFig.D.9,theparameter ais 1 because,bydefinition, scatteringdoesnot add pure direct radiation. Moreover, since soil reflections do not affect the pure direct radiation profile thecanopy sizedoesnot affect theradiation profile (apart from the fact that the curve for a canopy with a small LAI ends earlier the the curve holding for a larger canopy).  199  Appendices The parameter k subject to Eqn. D.l in order to describe the profiles shown in Figure D.9 reads k=0.89+0.26exp(-0.16 p). This parameter k is referred to in Appendix I asksunlit.  Relative intensity [-] 0.80.6-  0.4-  B = 1 5 °  VSy  0.2-  n-  0   .  B=35°  X ^ ^ w ,  0.5  .  l " i  1  "T  1.5  •  T  2  •  T  2.5  ~!  •  3  • l  "—-1—•—  3.5 4 4.5 cumulativeLAI[-]  FigureD.9Fittedandcomputedprofilesfor pure directradiation  200  Long-wave radiation  APPENDIX E: LONG-WAVE RADIATION  The emission of radiation by ablack body is described by the Stefan-Boltzmann equation: Eb = a T4  [Wm"2] (E.l)  WhereE,,istheemissive powerdensity oftheblack body(Wm'2), a theconstant of Stefan-Boltzmann (5.67-10"8Wm^K."4)andTtheabsolute surface temperature ofthebody(K). However, most natural bodiesarenotblack andradiate lessthan Eb.Therefore afactor e,theemissivity ofabodyisintroduced. It isdefined asthe fraction radiated energy compared totheradiative energyemittedbyablackbody at the same temperature. [Wm'2] (E.2)  E(V) = E(v)/Eb(v)  Whene(v) isconstant for allwavelength's v,thebody iscalled agrey body.Real bodieshavingaconstantemissioncoefficient overthewholespectrumhardlyexist butwhenonlyapart ofthespectrum isbeingconsidered, asinglevalue for ecan be applied. Since radiative heat exchange between elements in the greenhouse takes place in such a limited spectrum (5 - 50 urn), it is common in simulation modelstoassumeaconstantemission coefficient for thermal radiation(Takakura, 1992). Besidesemittance,theabsorbtion ofradiation isjustasimportant inradiativeheat exchange.Ablack body absorbs all incident radiation, regardless of spectral and directionalcharacteristics.Thustheabsorbtioncoefficient e(v)emission coefficient a(v) of a black body is 1over the whole frequency range. In general the absorbtion coefficient of a natural body is less than 1. It can be proved that for any particular body, the functions e(v) and a(v) are equal. This rule is known as Kirchhoffs law (Pitts, 1986). The remainder of the radiative energy to which a body is exposed is either reflected or transmitted. In radiation exchange, when there are more bodies interacting with each other, each body actsboth asanemitter and as anabsorber. In the following, thecalculus of such a radiative exchange is derived. Consider two parallel infinite opaque surfaces, having different emissivities and different temperatures. Theupper face of s2onlyradiates tos,. The lower face of S!only radiates to s,. »i  Tie, T2e2  Suppose an amount of energy E( is radiated from s, in the direction of s2. A fraction a 2 ofthisenergy isabsorbed bys2andtherest isreflected tos,.Thus p, 201  Appendices receives a fraction p2 back from itself. From this reflected energy an amount E[P2Pi scatteredbacktos2which againreflects tos,andsoon.Thetotalradiative energy transfer from s, tos2is: q"i,2= «2E,+a 2 p, p2E, +a 2 p, 2 p22E,+....+a 2 p, n p2nE, [Win2](E.3) Theothersurface (s2)isradiating inthesamewaytos,.Thetotalradiative energy transfer from s2tos, reads: q'Vi = a i E 2 + a i P2 PiE2 + «i P22Pi2E 2 + -  +a  i P2nPi"E2 [Wm"2] (E.4)  Both theexpressions areaseries resultingin:  The netradiation from s, tos2,being q",2 — q"2, is givenby:  Q-'u^f'""'^ 1 -  [Wm-2](E.6)  P1P2  With the assumption that the radiating surfaces are grey for the part ofthe spectrum where themajority ofenergy isradiated, Ecanbereplaced byEaT4. Also, assuming opaque surfaces and a comparable wavelength distribution of emittedandabsorbed radiation,therelation p=(1-a) =(1-e)holds.ThenEqn. E.6 can besimplified to: Q u ^ l / ^ W - 1  rWm-2](E.7)  Where Q'^2 represents thenetradiation flux from p, top2. If the temperature differences aresmall, this fourth-order equation canbelinearizedto:  QV^o/^VlVi  [Wm 2l<E 8)  " -  Where Tm represents themean temperature between T, and T2. The situation becomes more complicated when theradiation exchanging surfaces arenotinfinite. Radiation ofboth surfaces isdirected tothe total hemispherebut the intersection ofthe other surface with thehemisphere isjust a fraction. This fraction ofthe total radiation emitted by s4to which s3 isexposed iscalledthe view factor ofs4tos3(Notation F43). Likewise theview factor F34 isthe fraction of the hemisphere ofs3that intersects s4. Figure E.1. shows a sketch ofthe series of emission, absorbtion, and reflection between twofinite sized surfaces.  202  Long-wave radiation  absorbtion by s4 -•E,  F  3,4E3"> <—p4 F 3i4 E 3  - > «4F3,4E3  <~P4F3,4F4,3E 3 ~>P4 P3 F3,4F4,3E 3 P4P3 F3,42 F4,3E 3 - > <~P42 P3F3,42 F4,3E 3  - > a 4 P4P3F3,42 F4.3E 3  <-p42p3F3,42F4i32E3 - > p 4 2 p 3 2 F3,42 F4,32 E 3 P4 2 P 3 2 F3,4 3 F4,3 2 E 3 ->  2 ^ C  3c 2  - > «4 P4 P3 F3,4 F4,3 E 3  Figure E.l Radiative energy transfer from thefinite sized surface s} to the finite sized surface s4. From this sketch the following series can be derived describing the radiative energy flow from s3 to s4. q3j4=a4F3>4E3+a4p4p3F3,42F4>3E3 + a 4 p 4 VF 3 j 4 3 F 4 i 3 2 E 3 +....  [W] (E.9)  E 3 is determined by A 3 63a T 3 4 . The term A 3 is added because now we are not interested in energy flux densities but in the total energy flux. This is a consequence of the finite dimensions of s 3 and s4. If 0 < (p 3 P 4 F 3 4 F 4 3 ) < 1this series converges to: = q3 4  -  «4F3.4A3e3aT34 1 -(p3p4F3i4F4i3)  [W] (E.10)  The radiative energy flux from s4 to s3 can be determined analogue. After using the property that for finite body A 3 F 34 equals A 4 F 43 and that a equals e (Pitts, 1986) the net radiation from s3 to s4, being q 3 4 - q 4 3 yields: Q3 4  >  e, E4F, 4A-, a . 1-(P3P4 F 3,4 F 4,3) ( T 3  . T4>  [W](E.ll)  If necessary or for small temperature differences Equation E.l 1can be linearized analogue to Equation E.8.  203  Appendices  APPENDIX F: ESTIMATION OF THE SKY TEMPERATURE  Thehemispherearoundthegreenhouseisagaseousmedium consistingofparticles all having a certain temperature and therefore a certain electromagnetic energy emittance.Allparticlestogether, atdifferent altitudes inthesky,generate adownward radiation flux. Ontheother handtheopaqueelements onearth emitthermal radiation into the hemisphere. The net effect is a heat loss to the atmosphere. Thisnetheatlosscanbemeasured byapyrgeometer and,combined withthetemperatureoftheemittingelementofthemeasuringdevice,aActiveskytemperature (Tsky) can be computed. T sky = (T device 4 " R ^ * ) 0 " 2 5  M ( F1 >  withTdeviccthetemperature ofthemeasuring device,R„etthenetradiativeheatloss anda theStefan-Boltzmann constant(5.67-10"8Wm'2K'4).Obviouslytheemitting elementofthemeasuring device isassumedtobeblack.Thesky isopticallyblack by definition. If the sky temperature is not available in a set of meteorological data, several approximation algorithms canbe found intheliterature (Monteith, 1961; Sellers, 1965;Swinbank, 1963).However,contrarytotheapproachembedded inEqn.F.l, where aActivetemperature iscalculated inmeteorological literature itiscustomary to express the downward long-wave radiation flux as a function of a fictive emissivity oftheskyfrom whichthetemperature issettothetemperature atreference height (2 m). Thus the downward flux Rd is defined by R  d = Ssky° T air 4  [WnV2](F.2)  Meteorological literatureconcerningtheradiativeheatexchangetotheskyconcentrates on the parametrization of esky.It appears that esky,as applied in Eqn. E.2, iswell correlated withthevapour pressure atreference height. Brunt (1939)suggested arelation for clear skiesofthetypee=a+PJe, with ethevapourpressure. The parameters a and p differ from region to region. For moderate latitudes Monteith (1973) mentions eskv,c,a,= 0-53+ 6-10-3VPair0-5  [-] (F.3)  where the vapour pressure is expressed in Pa. The cold atmosphere is (partly) screened by optically black clouds with higher temperatures for cloudy skies.Monteith (1973) mentions the following empirical expression *sky = ^ . c l e a r O  +  " C2)  H (™)  where cdenotesthe fraction ofthesky covered bycloudsandncontributestothe different impact of the height of the clouds.For high clouds (for example cirrus 204  Estimationof thesky temperature types) the impact is low (n=0.04) and for low clouds (for example stratus, cumulus) the apparent emissivity is much more affected, expressed by n = 0.2. Monteith (1973)derived amoreconvenient expression fortheBritishIsles,where low clouds predominate over other cloud types. This empirical relation reads: Rd = (1 " c) s s ky,c,ea, CTT air 4 + < ^ J " 9)  [Win2] (F.5)  withctheclouded fraction of the sky.Because intheNetherlands lowcloudsare common aswell,Equation F.5 canbeappliedto estimate thedownward radiative flux. Expressing the downward flux with Equations such as F.2 and F.5 implies the calculation ofthenetthermal radiation bysubtracting Rjfromanupward fluxR„. The applied reasoning obliges the upward flux R„to be computed by Ru=eaT4 (with appropriate values for e and T). The radiative exchange processes in this study are computed using the theory presented inAppendix E.This approach computestheradiative heat exchangeas a function of temperature difference. Therefore, in the context of this work a Activesky temperature iscomputed by solvingthe black bodytemperature from the equation aTsky4 = Rj. Thus, using Equation F.5 the sky temperature can be estimated by Tsky = ( d - ^ s k y ^ T a i r ' ^ C T j - 9 / a ) ) 0 2 5  [K] (F.6)  205  Appendices APPENDIX G: GAUSSIAN INTEGRATION  Basically theGaussian integration method estimates themeanvalueofa function to be integrated within an interval of interest. With this mean value the integral of the function on this domain is simply the mean value multiplied by the width of the domain. To estimate the arithmetic mean of the function, the Gauss method samples the function on well chosen points. The more points are evaluated, the better the estimation of the integral. Supposeafunction istobesampled atonlyoneplacewithintheinterval.Thebest place to sample the function is inthemiddle ofthe interval. Indeed, polynomials up to the first order are integrated exactly by this method. Whentwo function evaluations inthe interval aretakentheGaussmethod selects these points in such a way that polynomials up to the third order are integrated exactly. Supposeafunction y=ax3+bx2+ex+dhastobeintegrated intheinterval-V2 <x<V2. Becausethelength oftheinterval is 1 theintegral ofthe function is the same as the mean of the derivative. When the two evaluation points are chosen symmetric around 0the sum oftheoddpowered terms ofthepolynomial become 0 because thepolynomial issymmetric in x=0. The analytic integral of the third order function in the interval <-*A,V%> is b/12+d. The mean of thetwo evaluations of the function to be integrated at x=-y and x=y is by2+d. The Gauss integration method statesthatby2+dhastobethesameasb/12+d.Therefore y is found to be 1A/12. The third order Gaussian integration performs three function evaluations to estimate the mean of the function and calculates the integral up to a fifth order polynomial exactly. The three evaluation points are placed symmetric around 0, resulting inthepoints x=0,x=-yand x=y. Contrary tothesecond order caseit isnotthe arithmetic mean ofthethree function evaluations torepresent themean value of the function but aweighted mean. Tofindthetwounknowns (y and the weighing term for the mid-point w), two equations can be defined. /Lv 2 -t-ft-..; 4- A A 2  1+ w + 1 (-y)4 + OAV+ (y)4_ 1+ w + 1  f'A.  J x"dx = 1/12  (G.la)  -'A  J x 4dx = 1/80  .v.  (G.lb)  The solution of this set of equation yields: y=-/0.15=> evaluation points:-0.387, 0, 0.387 w = 1.6=» weight of each evaluation: 1, 1.6, 1  206  (G.2) (G.3)  Gaussian integration Besidesasamethodtointegratepolynomials,Gaussian integration isalsosuitable to compute the integral of exponential functions, although for exponential functions the result is an approximation. Below gives an example by means of the computation of the integration of a non-polynomial function ex. J e x dx with the analytical solution e4 - e1 = 51.880  (G.4)  1  To use the three points Gaussian integration routine, three points relative to the middle of the interval have to be determined. x, =2.5-0.387-3 = 1.339  x2=2.5 x3=2.5+0.387-3 =3.661  (G.5)  Where2.5isthemiddleoftheinterval tobeintegrated (<1,4>) and 3isthelength oftheinterval.Nowtheestimation ofthemean function valuecanbedetermined: e1.339+,6  2.5+3.661  y=-—111.6+1  =17 280  -  (G7)  The last step is to multiply the estimated mean derivative by the length of the interval. 17.280-3 = 51.840  (G.8)  Comparing the numerical-found value with the analytical value shows that Gaussian integration gives avery good estimate ofthe integral of an exponential function.  207  Appendices  APPENDIX H: APPROXIMATION OF SATURATED VAPOUR PRESSURE  The saturated vapour pressure is dependent on its temperature. Many handbooks present tables on this quantity. Figure H.l shows the saturated vapour pressure curve for a temperature interval between -5 and 35 °C.  Saturated vapour pressure [kPa] 10 VP«,(0 = -274+ 878exp(0.0545t) 642-  o-10 -5  0  5  10 15 20 25 30 35 40 45 50 temperature [°C]  FigureH.1Saturatedvapourpressurecurve To beabletocomputethesaturated vapour pressure atanytemperature anexponential curve was fitted through thetable points.Thecurve-fitting resulted inthe expression: PsatuW= " 2 7 4 - 3 6 + 8 7 7 - 5 2 ex/7(0.0545 t)  [Pa] (H.l)  In the Figures H.2 and H.3 the absolute and relative deviations of the vapour pressures computed byEqn.H.l compared tothevaluesthrough which thecurve was fitted. From Figure H.3canbeseenthat inthemost important partofthecurve,namely the interval between 15and 25 °C, the error of Eqn. H.l is less than 1%. Besidesthesaturatedvapourpressurethemodel alsorequiresthederivative ofthe saturated vapour pressure function. The derivative of Eqn. H.l is easy to determine and yields: PsatuW = 47.82 ex/>(0.0545 t)  208  [PalC1] (H.2)  Approximation of saturated vapour pressure  Absolute deviation [Pa] 20 10-  0-3  Z  X  -10  X  X  '  1—'  -20 -30-j -40  1  -10 -5  "  1  1  0  1  5  '  1  '  !  1  »—I  "——I  i—l  '  1—•  10 15 20 23 30 35 40 45 50 temperature [°C]  Figure H.2Absolute deviation of the results ofeqn. H.1compared to table-values.  Relative deviation [%] 1-  0.8X  0.6-  X X  0.4-^  X  X  X X  X  X  0.2-^  n-  — i  i  -10 -5  . — i — i — i — ' — i — '  0  5  i — i — i — i  '  10 15 20 25 30 35 40 45 50 temperature [°C]  Figure H.3 Relative deviation of the results ofH.l, compared to table-values.  209  Appendices APPENDIX I: PHOTOSYNTHESIS  Given light in an appropriate spectral range, a canopy extracts C0 2 from its ambientinordertoproducestarchasanenergysource for itsgrowthanddevelopment. This chemical assimilation of sucrose from carbon dioxide and water is called photosynthesis. In the greenhouse climate simulation model the C0 2 consumption reflated to photosynthesis is referred to by the variable MCAirCan. Because photosynthesis is strongly non-linear the mean radiation intensity on canopy leaves gives insufficient information to compute the assimilation rate. Thus, in order to compute the canopy photosynthesis, the integral of the assimilation rates of the individual leaves must be based on local light intensities. In this section, first the leaf assimilation rate is related to the local radiation intensity. Then an approach to determine the distribution of light in the canopy stand ispresented, followed by a calculus for the canopy photosynthesis.  1.1 COz fixation in a canopy leaf Therate of C02-assimilation is an increasing function of radiation intensity. For low radiation intensities the response is almost linear, but at higher levels the process becomes saturated. Thus photosynthesis, as a function of irradiation, shows a maximum. It is described by (Gijzen, 1992): assim(VISabs) = P m jl-exp ( ' g p I S a b s ) }  [mgm-2ieafs'1](1.1)  Inthisfunction assim(VISabs)denotesthephotosynthesisperm2leaf,Pmthemaximalphotosynthesis(mgC02s"1m"2),etheinitiallight-useefficiency (mgC02J"')and VISabs the intensity of absorbed Photosynthetic Active Radiation (Wm"2). The initial light use efficiency depends onthe leaf temperature according to (Gijzen, 1992): e= e  0  a C  +2r  [mgC02J-*] (L2)  The variable e0isthepotential light-use efficiency inthe absence of oxygen and isreported to be 0.017 mg C0 2 (JVIS)"1 (Gijzen, 1992). The variable Ca is the C0 2 concentration oftheambient, expressed in ull"1, whichisequivalenttoaC0 2 concentration expressed in ppm. T is called the C0 2 compensation point and depends on leaf temperature. For air with anormal oxygen concentration (about 210 ml l'1) T is described by (Gijzen, 1992): T = 42.7 + 1.68(T, - 25) + 0.012(T, - 25)2  [ull 1 ](1.3)  In this equation the variable T,represents the leaf temperature (°C). 210  Photosynthesis The maximal rate ofphotosynthesis (Pg) depends onanotherthree variables.It is described by: [mgm-2leafs"1](1.4)  P g = Rd + min{Pn , P mm }  Rj is the dark respiration of the leaf (mgCC^m'V), Pn denotes the rate of net photosynthesis and Ymm, the endogenous capacity, limits the maximal rate of photosynthesis. The dark respiration is commonly determined by the Q10-factor. R  d = Rd,2oQ.o 01(Tl " 20)  [mgm-2leafs"'](1.5)  where Rj20 represents the dark respiration of a leaf of 20 °C. Gijzen mentions a value of0.05mgC0 2 m"2s"1.The Q10-factor describes the increment ofthedark respiration due to a 10°C temperature increase. Gijzen uses thevalue Q10=2. Therateofnetphotosynthesis (Pn)dependsonaC0 2 concentration difference and the resistance to diffusion of C0 2 . P  n - U 7 ^ 1 - 6 ^ r  c  [mgm^leafs"'](1.6)  The term 1.8 converts ppm to mg C0 2 . The multiplication by 1.37 converts the boundary layer resistance to vapour transport rbV, which was determined in Section 5.4.2,toaresistancetoC0 2 transport.Gijzen (1992)reported thestomatal resistance tovapourtransport (rs) tobe50sm"1for awiderange ofcanopies.The third resistance (rc) in theseries is a chemical resistance. In the work of Gijzen, this resistance is calculated from a chemical conductance (Cc). In his work Cc depends ontemperature. It grows linearly from 0to0.004 intheleaf temperature range from 5to 25 °C. Ontemperatures above 25 °C Ccdecreases linearly until thevalue 0 is reached at 40 °C. The value for rc is the reciprocal ofCc. The last parameter in the photosynthesis model is the maximal endogenous capacity (Pmm).According to Gijzen, Pmm is temperature dependent. Pmm is zero for temperatures beneath 5 and above 40 °C. Between 5 and 30 °C Pmmgrows linearly from 0to 2.5 mg C02m*2s''. In thetemperature range from 30 to 40°C ?mm decreases linearly from 2.5 to 0. mm  1.2 From leaf assimilation rate to canopy photosynthesis A canopy consists of numerous leaves that each intercept radiation at a certain intensity and thus induce a C0 2 consumption. With respect to the greenhouse climate simulation model the C0 2 consumption of allthese individual leaves has to be combined to a canopy assimilation rate. A fast and commonly used method toperform thecomputation of canopy photosynthetic activity from leaf photosynthesis is the Gaussian Integration method (Goudriaan, 1986) (see Appendix G). This numerical algorithm integrates a 211  Appendices function by the calculation of a mean value of the function to be integrated. For thethree-points GaussianIntegration thismeanvalueisdetermined byaweighted sumofthree functional evaluations, locatedontherelative distances 0.113,0.500 and 0.887 of the domain for integration. Inthecaseofdetermination ofcanopyphotosynthesisthefunction tobeintegrated is the photosynthetic activity, which, by means of the declining intensity of radiation, depends ontheheight in canopy. The domain of integration isthetotal leaf area, which is expressed by the LAI. Thus, calculation of canopy photosynthesis by Gaussian Integration isperformed by aweighed sum of photosynthetic activity in three levels of the canopy, multiplied by the LAI. The photosynthetic activity at a certain level in the canopy is a function of the absorbed radiation onthat level.The simplest way todetermine theabsorbtion is to consider the change of radiation intensity through the canopy to be partly caused by absorbtion, andpartly by scattering. The change of radiation intensity at an arbitrary height in the canopy isthe derivative of the exponential function describing the radiation profile. dl vis (x) = -k I V I S e"kx L A I  [Wm-2](1.7)  In this equation the extinction coefficient (k) has different values for different types of radiation (diffuse or direct) and LAI (see Appendix D). IyiS is the intensity of radiation at the top of the canopy and x is the relative depth of the considered canopy level,counted from thetop.Asshown inAppendixD,IV]Scan be even larger than the radiation flux in the visible wave band entering the greenhouse (see the discussion on Fig. D.5). The rate of change of the intensity of radiation originates from absorbtion and reflection ofradiation bythecanopy.Thus,multiplication ofthederivative ofthe radiation profile with anabsorbtion coefficient yieldstheabsorbed radiation flux. This flux is defined in Eqn.1.8. VTC.bs.difM = adifkdifW f «P(-k dif xLAI)  [Wm'2](1.8)  The ' - ' sign from Eqn. 1.7has disappeared because the absorbtion of radiation has asignoppositetothedecrement of light intensity.The absorbtion coefficient for diffuse radiation (adif) can bededuced from the work of Goudriaan (1977) as being defined by:  With a scattering coefficient (sc) 0.15, which is a common value for a canopy stand (Goudriaan, 1977), Eqn. 1.9yields a dif =0.71. The computation oftheabsorbtion ofdirect radiation ismore complicated. Inthe firstplacetheextinction ofdirect light isstrongly dependent ontheangleofsolar 212  Photosynthesis elevation. These dependencies are discussed inAppendix D. In the second place thescatteringofdirectradiationafter interceptionbyaleafsurface induces diffuse radiation. Thusthe decrement of light intensity from direct radiation is lessthan the decrement of direct irradiated leaves. To compute the amount of secondary diffuse radiation,theprofile ofpuredirect radiation issubtracted from the profile describingthetotalradiation intensityfromdirectradiation. Callingtheextinction coefficient of the full direct profile kdir(P), the diffuse radiation flux induced by scattering of direct radiation is expressed as: V  ISabS)dir-Klif(x.P) =IVIS>dir(kdir(P)^(-kdir(P) x L A I ) t W m ' 2 ] 0-10) -k s u n , i t (P)^(-k s u n l i t (P)xLAI))  Again xdenotesthedepth ofthecanopy layer under consideration. The radiation flux VISabsdir^,if acts the same as thepreviously defined VISabsdif. Thus the total amount of absorbed diffuse radiation is described by: VIS  abs,dif,tot(x) = VIS abS)dir ^, if (x) + VIS absdif (x)  [Wm-2] (LI1)  Athird complicating factor oftheabsorbtion ofdirect radiation isthatthroughout thecanopy depth,thesunlit surfaces areall irradiated atthesame intensity.Thus, theprofile of pure direct radiation israther adescription of thefractionof sunlit leavesthan a representation of the intensity of the direct radiation. In a formula: frsunlit(x,P) = ^ - k s u n I i t ( P ) xLAI)  [-] (1.12)  Thecomplement ofthesunlitleavesareleavesintheshade.Theseleavesintercept diffuse radiation only.Thustheassimilationrateofleavesintheshadeatarbitrary height in the canopy is described by: MCshade(x) = (l-frsunlit(x)) assim(VIS absdiftot (x))  [mgs-'rn2] (1.13)  As far as the sunlit leaves are concerned a fourth and final complicating factor withrespecttodirectradiation mustbesolved,namelythelargeunevennessofthe anglebetweenthebeam ofdirect radiation andthenormal of sunlit leaf surfaces. Thisangle©determines the 'dilution' ofthebeam ofradiation atthecanopy surface. When the angle is zero, the leaf surface is positioned perpendicular at the solarbeam,whichresults inintensitiesofirradiation uptoabout 500Wm"2.When the angle is large, the beam of radiation is spread out over a large leaf surface. Thusthisradiation is'diluted'. Dependingonthesolarelevation andthegeometry of the canopy, afractionaldivision can be made amongst the leaf surfaces irradiated with a certain dilution factor. In Table 1.1the relative frequency of these dilution factors for a number of solar elevations is presented.  213  Appendices Table1.1 Relative frequency of dilution factors (roundedto onedecimal) for directradiation onacanopywithaplanophile leafangle distribution for anumberofsolarelevation angles. dilution factor (cos(co)) 0.7 0.5 0.6  p  0.1  5 15  0.097 0.074 0.064 0.045 0.029 0.015 0.003 0.127 0.096 0.071 0.053 0.039 0.025 0.008 0.208 0.137 0.100 0.079 0.057 0.044 0.017 0.097 0.136 0.213 0.113 0.101 0.065 0.036 0.064 0.086 0.128 0.235 0.156 0.117 0.058 0.035 0.028 0.034 0.046 0.061 0.089 0.134 0.276 0.202 0.095 0.018 0.016 0.025 0.032 0.048 0.070 0.108 0.171 0.357 0.155  25 35 45 55 65  0.2  0.3  0.4  0.8  0.9  1.0  0.368 0.174 0.133 0.206 0.183 0.192 0.138 0.098 0.123 0.090 0.067 0.080 0.060 0.044 0.053  In thetable, thefrequency ofdilution factors smaller than 0.05areadded to the first column, which isagood approach sincethefirstpart ofthe photosynthetic response-curve ispractically linear. With data from Table 5.1, the carbon dioxide fixation by sunlit leaves canbe expressed as 10  MC ..  sunlit(x>=frsunlit(x) I WW) assim(VlSabsdir(i))} 1=1  [mgm-V1] (1.14)  '  with  ^ W r W =*dirVISdir±™ + Us.dif.tot where MCsuniit denotes theassimilation rate ofsunlit leaves,frsunli,thefraction of sunlit leaves, f(P,i) the fraction of the sunlit leaves intercepting direct radiation withanintensitywhichisafactor i/10ofthe radiation perpendicular onthe direct beam,adirtheabsorbtion coefficient ofleavesandVIS diri theintensityofradiation perpendicular tothedirect beam. The factor i/10 dilutes VIS diri and VISabsdiftot adds thediffuse radiation tothetotal amount of radiation onthesunlit canopy leaf. From thework ofGoudriaan canbededuced that adirequals 0.82for radiation inthevisible range ofwavelengths. UsingtheGaussian integration method, thecanopy assimilation rate cannow be found from MC Ai,Can = < °- 2 7 8 (MCshade(°-lD+ MCsunlit(0.11)) [kgm'V] (1.15) +0.444(MCshade(0.50)+MCsunlit(0.50)) + 0.278(MCshade(0.88)+MCsunlit(0.88)) } MO"6LAI In this equation 0.278, 0.444and0.278aretheweighing factors ofthe contribution ofthe photosynthesis at0.11, 0.50and0.88ofthe canopy depthtocompute the mean photosynthetic activity per m2 leaf area. Multiplication with the LAI yields thecanopy photosynthesis. Theterm 1-10"6converts mgto kg. 214  Solarelevationandazimuth APPENDIX J: SOLAR ELEVATION AND AZIMUTH  The position of the sun in the sky vault is defined by its azimuth and elevation. The azimuth is the angle between the sun and the geographical south, measured on ahorizontal plane.The angle between the sun and that plane isthe elevation. If the orbit of the sun was a perfect circle, the azimuth could be computed from thetimeofday asafraction of 24hours.However, because theorbit oftheearth around the sun is an ellipse, the time at which the sun reaches its highest point, correspondingwithanazimuth 180,iseithersomewhat advancedorretarded.This advanceorretard iscalled theequationoftime.Anempirical formula tocompute the equation of time reads (France and Thornly, 1984): At=-7.13cos(y) - 1.84 sin(y) - 0.69cos(2y)+9.92sin(2y)  [min] (J.l)  with ythe year angle. The year angle iszero at thevernal equinox on 21March. Thus the year angle can be expressed as a function of day number by: y= 360 (c/aynr-80)/365  [°] (J.2)  with daynrthe sequential day of year, counted from January 1st. With Eqn. J.l, the azimuth as a function of time can be expressed by: az = 360 (Ar+At/60-12)/24  [°] (J.3)  withhrthelocal solartime.Duringwintertime,the local solar time ofaplaceat a specific longitude is a factor 24-longitude/360 hr less than the local middle European time. During summer time the local time is another hour less. The solar elevation can be expressed as a function of the latitude, the actual azimuth and the solar declination (8). The solar declination isthe angle between the linejoiningthecentres of thesunandtheearth, andtheequatorial plane.The declination angle depends on the day of year (expressed with the year angle y) according to (France and Thornly, 1984): 8 = 0.38 - 0.77 cos(y) + 23.27 cos(y)  [°] (J.4)  When (J> denotes the latitude, the sine of the elevation angle (Q is expressed by (France and Thornly, 1984): sin(Q = sin(<|>)sin(8) + cos(<|>)cos(S)cos(az)  [-] (J.5)  from which the elevation follows from the arcsine of Eqn.J.5.  215  Appendices APPENDIX K: NOTATION  A surface (m2) A0 surface of a window (m2) (see Figure 5.4) I radiation intensity (Wm"2) LAI leaf area index [-] 1 length of a heatingpipe per m2 floor surface (m"1) I characteristic dimension of a canopy leaf (the width) (m) (Eqn. 5.56) d diameter of a heating pipe (m) r resistance (sm'1) T temperature t time (s) ts step size in a numerical integration procedure (s) C02 partial carbon dioxide pressure (Pa) C forced carbon dioxide flux (kgs"'m"2) HEC heat exchange coefficient (Wm'2K"') k extinction coefficient MTC mass transfer coefficient (kgs'Im"2Pa'1) N number of cells in the shift register representing the storage tank (-) P forced heat flux (Wm-2) r resistance sm'1 REC radiative heat exchange coefficient (Wm^K-4) SC screen closure fraction (-) SO absolute screen opening (m) (see Figure 5.5) u wind speed (ms"1) v velocity of water through a heat distribution loop (ms'1) VP partial vapour pressure (Pa) W gutter to gutter distance (m) (see Figure 5.5) x moisture content (gkg'1)  216  Notation Greek symbols a (} y AH e 9 X i v p o O O* <|) <j>" vj/ © 9  heat exchange coefficient (Wm" 2 K"'); absorbtion coefficient (-, Appendix E) thermal expansion coefficient (K"1), solar elevation angle psychometric constant (65.8 Pa K'1). heat of evaporation (2.45 -106Jkg"1). long-wave emission coefficient (-) window-opening angle, relative to the roof (degrees) (see Figure 5.4) air factor (-, Chapter 4);thermal conductivity (WmK'1, Chapter 5) partial massfraction ofconstituentsofexhaustgasesofcombustion devices kg per m3 combusted gas) wavelength (m) density (kgm"3);reflection coefficient (-, Section 5.5.2.3,Appendix E) Stefan Boltzman constant (5.67-lO" 8 Wm^K" 4 ) combustion rate ofnatural gas (m 3 natrural gas per second) combustion rate ofnatural gas normalized tothe greenhouse floor surface (m 3 natrural gas per second per m 2 ). air flux ( m V ) flux per m 2floor surface (m 3 m" 2 s"') or (Wm' 2 ) roof slope ofthe saw-tooth greenhouse cover (degrees) (see Figure5.4) angle (radians) mass flux ofwater through heating pipes, normalized perm 2 greenhouse surface (kgm'V)  Dimensionless numbers Le Nu Gr Ra LAI Pe  lewis number nusselt number grashoff number raleigh number leaf area index Peclet number  217  Appendices Subscripts air  greenhouse air compartment. When the thermal screen is opened the greenhouseaircompartment represents alltheairintheenclosure.Ifthe thermal screen isclosedtheaircompartment representstheairbelowthe screen only. alu artificial illumination b boundary layer can canopy cov greenhouse cover d downward do lower side flr greenhouse floor H heat i internal indices ij low lower heating pipe NIR short-wave radiation in near infra red waveband out outside pip heating pipe scr thermal screen i*' storage tank compartment sti sol..so6 first up to the sixth soil layer so7 boundary condition in the soil top air compartment above the screen. u upward up upper side upp upper heating pipe V vapour VIS short-wave radiation in the visible waveband  218  Summary SUMMARY During the past two decades, the production per m2 floor surface of glasshouse horticulture intheNetherlands has almost doubled. Besides improvements of the greenhouse construction, the genetic properties of the plant and its nutrition, an important factor contributing to this increment is the improved control of greenhouse indoor climate. C0 2 supply and artificial illumination have become particularly widespread and the growth season has been lengthened. Coupled to the intensification of the production process, the mean energy consumption per m2 greenhouse surface shows a steady increment of (0.05 GJm"2year"' per year during the last 5years). For the current glass covered area of almost 11-103hectare,this means ayearly extra energy consumption of 5PJa. Together with the growth rate of the glass covered area of som 175hectare per year, the total primary energy consumption of horticulture in the Netherlands increases with some 7 PJ per year. In 1993,theprimary energyconsumption ofhorticulture was 138PJ,which is5% of the domestic energy consumption. Because ofthe growing concern abouttheeffect oftheincreasing carbon dioxide concentration in the atmosphere, which is strongly related to the combustion of fossil fuels, the government of the Netherlands aims to diminish primary fuel consumption. In order to reach that goal, agreements have been made with all energy intensive sectors of economy. Representatives of horticulture in the Netherlands have formulated a target with respect to energy conservation. This target is to cut the primary energy consumption per unit of production valueby half by the end of the century compared to its value in 1980. The official agreement, henceforth referred toastheMJA(Meerjarenafspraak), also included the definition of a measuring unit that enables this target to be monitored. This measuring unit is referred to as ENSEC (Economically Normalized Specific Energy Consumption). By an economic normalization of the production, the course of the ENSEC can be computed for any mix of horticultural products. In Chapter 2 the definition of ENSEC is presented and the course of ENSEC duringtheperiod 1980to 1993isshown.ItappearsthatENSEC's tendency, after a rapid fall in theperiod 1980 to 1985,is to remain constant at around 65.This level is quite far from the stated objective (an ENSEC=50 in the year 2000). Moreover, when extrapolating thetendencies of the last 5for theprimary energy consumption and production value per m2 greenhouse, ENSEC can be expected to grow to 72 in the year 2000. Thus, in order to reach the target, the current tendencies have to change direction. "1PJ = 1-1015J which is equivalent to about 32-106m3 of natural gas. 219  Summary Principally, the decrement of the ENSEC can be achieved by a decrement of primary energy consumption or by an increment of production. However, it has been shown for the second case that the general governmental objective to decrease theabsolute level ofC02-exhausta, will be severely violated, providing that the current tendency of increment of the glass covered area persists. Therefore, measuresproposed intheMJAtoachievetheagreedtargetare focused ontheother factor that determines the ENSEC;thedecrement of primary energy consumption. From the 25 measures that are proposed, nine subjects to be evaluated on their energy saving prospective are selected. These subjects are arranged into three groups.Thefirstgroupconcerns simple measures withrespect tothe engineering of the heatingsystem that can bereadily applied. The second group involves the improvement of the greenhouse building by the decrement of leakage and by improving the degree of insulation of the covering structure. The third group includes energy conserving heating devices. In this group the potentials of a condenser, a short- term heat storage facility and a combined heat and power engine are evaluated. The energy saving effects of the selected measures are difficult and time consuming tostudy ina working greenhouse. Difficult because it isvery hard to exclude effects from other factors than the measures to be studied and time consuming since the experiments should span at least one year. Therefore, a method is needed thatjudges energy-saving techniques for modern horticultural practice in an unambiguous and reconstructible way. To serve this need, in this study a deterministic simulation model is developed that describes the energy consumption ofamodern greenhouse, accounting forthetypicalcharacteristics of the indoor greenhouse climate,the greenhouse climate controller andthe heating system. In Chapter 3 the requests on such a simulation model are presented. From these requests itisdeduced that theprimary statevariables tobe described concern the heating pipe temperatures, the indoor air conditions with respect to temperature, humidity and C0 2 concentration and the temperature at the top and bottom side of theheat storage tank. To describe the dynamics ofthese entities, anumber of other state variables are defined. Also the boundary variables on the model are presented. In order to be able to keep up with the dynamics of modern greenhouse climate controllers, itisargued that the simulation model requires aresolution intimeof  "Thegeneralgovernmental objectivetodecreasetheC02-exhaustaimstohave decreased theexhaust atthe endofthecentury to96%of itsvalue in 1990for all energy intensive sectors of economy. 220  Summary up to one minute. In order to create easy interpretable parameters and to ensure that the model can be applied in numerous variations, it was decided to develop adeterministic model.Asanintroduction tothedetailed description ofthemodel developed, the essentials of the selected model type are presented. Thepresentation ofthe developed model isdivided overtwo chapters. Chapter4 describesthecomponentsoftheheatingsystemsimulation,theconnectionofthese components to each other and the connection oftheheating system simulation to the greenhouse climate simulation model. For each of the components in the heating system a sub-model that describes the characteristic behaviour of the device is presented. In Chapter 5 the greenhouse climate simulation model is presented briefly but integrally. Unlikethegreenhouse heatingsystem simulation (Chapter 4),the greenhouse climate simulation model proceeds from the current state-of-the-art.  The connection between the heating system (model) and the greenhouse climate (model) can be seen as being performed by the greenhouse climate controller. Therefore, Chapter4beginswithadescription ofthefunctionality ofacustomary greenhouse climate controller. The controller attempts to achieve asetpoint with respecttoairtemperature, humidity andC0 2 concentration. Therealization ofthe temperature setpoint is performed by heating or ventilation. Ventilation is also appliedwhenthehumidity exceedsacertainthreshold. Inthatcase,iftemperature of the outside air is below the greenhouse air temperature, this results in a heat demand aswell. Therealization of aC02-concentration isperformed by exhaust gases supply. Thus, temperature control and, indirectly, humidity control induce aheatdemand. Eventually theheatdemand causescombustion ofprimary energy (natural gas)bytheboiler orCHP engine.C0 2 supply alsoforces thecombustion of primary energy. Intheheating system simulation model sixcomponents aredistinguished namely the heating circuit, the boiler, the condenser, the CHP-engine, the heat storage tank and the expansion vessel. From thepoint of view ofthe model concept, the simulation ofthe expansionvessel couldbeomitted. However, thisdevice isstill discussed here because one of the energy-saving measures mentioned in MJA concerns the expansion vessel. In order to describe the dynamics a horticultural heating circuit, which from horticultural pointofviewisthemajor component oftheheatingsystem,amodel hasbeen developed thattakes account of its special characteristics. The model is compared to detailed measurements in a semi-practical research facility. The results of the model show a good resemblance with the measured values. Itwasargued that adescription ofthedynamics of aboiler isnotrequired for the present purpose of the model. However, since the insulation of the boiler is one 221  Summary oftheenergy-savingmeasuresproposed intheMJA,therelationbetweenheatloss and insulation thickness is determined, on the basis of general theory on heat exchange. Withrespecttothecondenser itisknownthattheenergy savingachieved depends on thetemperature ofthewater fed tothe device,thevolume flux of the exhaust gasespassing the condenser and the combustion characteristics of theboiler. On behalf of the present heating system model these relations are quantified. The CHP-engine isdiscussed briefly because, asargued inthiswork, theheating system model considers its reject heat as an on/off heating power. The energy-saving prospectives oftheheat storage tank isoneofthemajor items of the energy saving measures to be evaluated. Therefore, with respect to the present study, an extensive model describing its dynamics has been developed. The model results are compared to measurements. The comparison shows that both charging and discharging of the storage tank are well described. Finally, in Chapter 4 the devices in the heating system are connected to each other. The dynamic behaviour of this entire heating system is shown in some graphs. In Chapter 5 the greenhouse climate simulation, which isthe second component of the model, is presented. The simulation model includes the application of thermal screens and artificial illumination. Thegreenhouseclimatesimulationmodelisdividedintothreeparts.Thefirstpart concernsthedescription oftheC0 2 concentrations inthegreenhouse.Thesecond part describes themodelling of humidity of the greenhouse air. The third part of the model comprises the thermal part of greenhouse climate simulation. The relations described in Chapter 5 are derived from the recent literature on greenhouse climate modelling. In Chapter 6 the results of the aggregated simulation model are compared to detailedmeasurementsmadeinaresearch facility,whichservesasasemi-practical greenhouse. A rose canopy was grown in the research facility. From August to April artificial illumination was applied, subject to a customary illumination control.First, comparisons onasmalltime scalearemade for ashortperiod.This means that ten minute mean values of greenhouse air conditions with respect to temperature, humidity and C02-concentration, heating power and pipe temperatures were compared with measured values, gathered on three successive days. The values anddynamics ofthemodelled quantitieswerevery much the same as the measured values, although sometimes distinct differences could be noticed. Also the climate controller actions with respect to window aperture, the closure ofthethermal screen andillumination control were almost equaltotheregistered control actions. The control of C0 2 supply showed some differences with the 222  Summary control in the research facility. On ayear round time scale,the daily mean greenhouse air temperature waswell simulated, except during very warm periods. During those periods the modelled temperature was higher than the measured value. Also the modelled daily water consumption wascompared withtheregistered water consumption. In springand summerthemodel over-estimated thedailyevaporation,butinautumn andwinter the daily water consumption was simulated well. The year round result with respecttoheatdemandofthegreenhousewasmodelledwithanaccuracy of98%. After the model quality is shown by comparing its results with results from the small research facility, the simulation model is applied to the study of energy savingpotentials ofthemeasures selected from the optionsproposed intheMJA (Chapter 2).Todoso,themodel isre-parametrized sothat itrepresents amodern greenhouse of 1 hectare growing tomatoes intheNetherlands. Its heating system is supposed to be equipped with a condenser and a heat storage tank of 80m3. For this reference greenhouse, a set of customary greenhouse climate controller settings isdefined. The controller settings are suitable for atomato crop,planted on 1 December and removed on 15November. Furthermore, with respect tothe modelsboundary variables asetof weather data ischosen that can be considered representative of typical weather in theNetherlands. The first group of energy saving measures to be studied consisted of relatively simpleimprovements totheboilerhouse,involvingtheincrement oftheinsulation thicknessoftheboiler,theinsulationoftransport pipesandthereplacement ofthe place of connection of the expansion vessel. With respect to the computation of the effect of the insulation of transport pipes, six pipe types are defined. These have been distinguished according to their function in the heating system. The savingsachievedbyreplacingtheattachmentoftheexpansionvesselarecomputed for the reference greenhouse (including a heat storage tank) and a greenhouse without a storage tank. It appears that the energy savings achieved by these simple measures are small. However, sincetheproposed measures areeasy,andtherefore relatively cheapto implement they can still be advantageous. The second item of energy-saving measures studied with the simulation model concerned the decrement of energy losses from the greenhouse cover by thedecrement of leakage through windows,theapplication ofathermal screen andthe application of alternative cladding materials (coated glass panes and double glazing). Under the circumstances created to study the effect of the prevention of leakage through windows the decrement of heat demand was small (1.6%). The other measures show energy savings ranging from 18% (a tin-oxide coating) to up to 47% (an option using double glass where each glass is coated with a tin-oxide 223  Summary coatingand aparticular polymer coating). However, thethermal screen andmost of the alternative cladding materials result in a decreased transparency of the greenhouse.Thisresultsinadecrement ofphotosynthesis.Tocombinetheenergysaving effect with the loss of production, the qualities of the thermal screen and the alternative cover materials are rated according to their impact on the decrement ofspecific energyconsumption.The specific energy consumption is defined astheyearlyamountofprimary energyrequired perunitofyearlyphotosynthesis. Withrespect tothespecific energy consumption the achieved savingsrangefrom 10% (a tin-oxide coated cover) to 39%(double coated double glass). An interesting aspect of increasing insulation properties ofthe greenhouse cover isitseffect ontheincreaseofthe(absoluteandrelative)portionofenergydemand related to dehumidification of the greenhouse. This effect is quantified for each of theoptions discussed withrespect to measures inthe second item.The results showthattheportion isaboutdoubled for the greenhouse withthebest insulated cover, compared to the reference greenhouse. Thethird itemofenergysavingmeasuresconcernstheapplication ofacondenser, a short-term heat storage facility and a combined heat and power engine. The condenser is studied for two configurations. It appears that it isadvantageous to beabletofeed thecondenser withreturn water from bothheatingcircuits instead of a connection solely to the lowtemperature heating circuit. The effects of aheat storagetank isstudied for a greenhouse with and without a CHP engine. As far as a greenhouse without a CHP engine is concerned, the storage tank is used to carry reject heat from C0 2 supply from the day to the night. Depending on the C0 2 supply strategy, the storage tank appears either mainly to affect theprimary energy consumption or mainly theyearly photosynthesis.Energy is saved if the C0 2 is generated by the combustion of natural gas irrespective of theheat demand. For this strategy the storage tank diminishes the occasions that heat surpluses have to be carried off by extra ventilation. If the supply strategy prevents heat surpluses havingto be carried off, the implementation of a storage tank does not save primary energy, but enhances the yearly photosynthesis.Again,tocombinebotheffects theprospectsofaheatstoragetank arejudged on its impact on the decrement of specific energy consumption. For both supply strategies, the specific energy consumption as a function of storage tank dimension was computed for three C0 2 supply rates. In a greenhouse with a CHP engine for electricity demand for its artificial illumination, astoragetank affects boththeprimary energy consumption and the yearly photosynthesis (assuming a C0 2 supply strategy that avoids extra ventilation). It is shown that the second effect dominates the first. In the situation where the CHP engine serves the electricity production of the public grid, the major factor that determines the primary energy saving is the 224  Summary thermalpowerofthedevice.Heretheenergysavingsemanatefromthedecrement of electricity to be produced in public power plants as a part of the public electricity demand is produced by CHP engines in horticulture. It is shown that large energy savings of upto 32%can be achieved. If exhaust gases of the CHP engine can be cleaned to such an extent that they can serve the C0 2 demand of a greenhouse the prospects are even more promising. In Chapter 7the conclusions of this study are presented and discussed.  225  Samenvatting SAMENVATTING In de afgelopen twee decennia is de produktie per eenheid kas-oppervlak in de Nederlandse glastuinbouw ongeveerverdubbeld. Dezegrotetoename isnaastverbeteringenaandekasconstructie,degenetischeeigenschappenvanhetplant-materiaal en een verbeterde voeding, voor een belangrijk deeltoe te schrijven aan de conditionering van het kasklimaat. C02-dosering enassimilatiebelichtingworden op uitgebreide schaal toegepast en de gemiddelde teeltperiode is verlengd. Gerelateerd aandezeintensiveringvanhetproduktieproces ishetgemiddeld energieverbruik gestaagtoegenomen (0.05GJm"2jaar'' perjaaroverdelaatste5jaren). Bijhethuidige glastuinbouwareaal vanruim 10-103hectare betekent diteenjaarlijks extra energieverbruik van 5PJa Samen met een areaal-groei van ongeveer 175 hectare per jaar neemt het primaire energieverbruik (fossiele brandstoffen) jaarlijks met ongeveer 7 PJ toe. In 1993bedroeg het totale energieverbruik in de Nederlandse glastuinbouw 138 PJ, waarmee de sector verantwoordelijk is voor ongeveer 5% van het jaarlijks nationaal energieverbruik. Vanwege de groeiende zorg om het effect van een stijgende C02-concentratie in deatmosfeer, watsterk gekoppeldisaandeverbrandingvanfossiele brandstoffen, heeft deNederlandse overheid het doelgesteld hetgebruik vandeze brandstoffen te doen verminderen. Met alle energie-intensieve economische sectoren heeft zij daartoe convenanten afgesloten. Indeglastuinbouw heeft zo'n convenant gestalte gekregenindeMeerjarenafspraak-Energie voordeNederlandseGlastuinbouw(in hetvervolg aangeduid met MJA).Deconcrete doelstellingmetbetrekking tothet gebruikvan fossiele brandstoffen iseenhalveringvanhetprimair energieverbruik per eenheid produkt inhetjaar 2000tenopzichte van 1980.Om derealisatie van dezedoelstellingtekunnenbeoordelen isindeMJAeenmeet-eenheidovereengekomen.Dezemeet-eenheid, die in ditproefschrift met ENSECb wordt aangeduid geeft het percentage van de waarde van het actuele primair energieverbruik per eenheid produkt ten opzichte van de waarde van deze breuk in 1980. De doelstelling van de MJA is dus een ENSEC=50 aan het eind van de eeuw. De weeg-factor van de verschillende glastuinbouwprodukten in de ENSEC is gebaseerd op hun onderlinge waarde-verhouding. Inhoofdstuk 2wordt dedefinitie vandeENSEC indetailbesproken enwordthet verloop van deENSEC over deperiode 1980tot enmet 1993 gepresenteerd. Het blijkt dat,naeen aanvankelijk sterke dalingindeperiode '80-'85,deENSEC gea  l PJ = 1-1015 J en komt overeen met de vebrandingswaarde van ongeveer 32-106m3 aardgas. b Economisch genormaliseerd specifiek energieverbruik 226  Samenvatting durende de laatstejaren constant rond de 65 isgebleven. Bovendien, wanneer de tendensen met betrekking tot energieverbruik en produktie van de afgelopen 5 jaren worden doorgetrokken, komt de ENSEC in 2000 uit op 72. Om de doelstelling van de MJA te halen zullen de huidige trends dus moeten worden omgebogen. In principe kan een verkleining van de ENSEC zowel worden bereikt door een verminderingvanhetprimair energieverbruik alsdoor eenvergroting vandeproduktie.Echter, bij eenvermindering vandeENSEC middels produktie-verhoging zal, bij voortzetting van de huidige groeivoet van het glastuinbouwareaal, de algemeneC02-doelstellingdiedeoverheid heeft gesteld"bij langenanietworden gehaald.Daarom isalleaandacht indeMJA gericht opeenvermindering vanhet primair energieverbruik. Van de 25 energie-besparende opties die in de MJA genoemd worden, zijn er negen inhet kader vandit proefschrift bestudeerd. Dezenegen opties zijn indrie clustersgegroepeerd. Heteersteclusteromvatmaatregelen rondhetverwarmingssysteem dieeenvoudigkunnenworden toegepast.Hettweedeclusterheeft betrekking op maatregelen die dewarmteverliezen van de kasconstructie verminderen. Het derde cluster betreft energie-besparende installaties zoalseen condensor, een warmte-opslag tank en een warmtekracht installatie (WKK-installatie). Debestuderingvandeeffecten vandegeselecteerdeenergie-besparende optieskan moeilijk ineenpraktijkexperiment worden uitgevoerd,omdat andere invloedsfactoren dan de bestudeerde optie haast niet uit te sluiten zijn. Bovendien zou zo'n praktijkexperiment tijdrovend zijn omdat voorveelmaatregelen een goedoordeel paskanworden gegevennabestuderingvaneenjaarrondsituatie. Daarom iserbehoefte aaneenmethodewaarmeedeeffecten vanvoorgestelde energie-besparende maatregelen indetuinbouwkundige context eenduidig kunnen worden ingeschat. Teneinde in deze behoefte te voorzien is er in het kader van dit proefschrift een deterministisch simulatiemodel ontwikkeld dat het energieverbruik van een moderne kas berekent in afhankelijkheid van de specifieke eisen aan het kasklimaat, de werking van de kasklimaatregelaar en de bedrijfsuitrusting met betrekking tot hetverwarmingssysteem. Inhoofdstuk 3worden deeisendieaanzo'n model moeten worden gesteld geformuleerd. Uit deze eisenwordt afgeleid dat het simulatiemodel in eerste instantie een beschrijving vereist van de pijptemperaturen in de verwarmingsnetten, de kasluchtconditiesmetbetrekkingtottemperatuur,vochtgehalteenC02-concentratie  "InhetNationaalmilieubeleidsplan-plus(1989)heeft deoverheidzichtendoel gesteld de C02-uitstoot in het jaar 2000 voor elk van de energie-intensieve economische sectoren terug tehebben gebracht naar 96%van de uitstoot van de betreffende sectoren in 1990. 227  Samenvatting en de watertemperatuur boven- en onderin de warmte-opslag tank. Omhetdynamisch gedragvandezegroothedentekunnenbeschrijven, wordeneen groot aantal andere toestandsgrootheden gedefinieerd. Ookworden devariabelen die aan de systeemgrenzen op het model worden gelegd toegelicht. Tenslotte worden, als aanzet tot de gedetailleerde beschrijving van het simulatiemodel, de essenties van het gebruikte modeltype besproken. Hetontwikkeldesimulatiemodel wordtbeschreven inhoofdstuk 4en5.Hoofdstuk 4beschrijft decomponentendieinhetkasverwarmingssysteemzijn onderscheiden, de onderlinge koppeling van deze componenten en de koppeling tussen het verwarmingssysteem simulatiemodel en het kasklimaat simulatiemodel. Voor elke component van het verwarmingssysteem wordt een sub-model geformuleerd dat hetspecifieke gedragvandiecomponent beschrijft. Inhoofdstuk 5wordt hetkasklimaatsimulatiemodel kort doch integraal beschreven. De beschrijving is kort omdatditdeelvanhetmodel,integenstellingtothetverwarmingssysteem model, gebaseerd is opkasklimaatmodelbeschrijvingen in de literatuur. In het modelconcept wordt de koppeling tussen het verwarmingssysteem(model) enhetkasklimaat(model)verondersteldtewordengerealiseerddoordekasklimaatregelaar. Daarom begint hoofdstuk 4 met een beschrijving van de essentie van gangbare kasklimaatregelaars. De kasklimaatregelaar tracht een temperatuur, vochtigheid en COz-setpoint te realiserenmiddelsverwarming,ventilatieenC02-dosering.Ventilatievindtplaats op grand van temperatuur- of vochtcriteria. C02-dosering wordtverondersteld te worden gerealiseerd middels ketelrookgassen. Deregeling vanhet kasklimaat zal dusresulteren in eenwarmtevraag dieopeen of andere manier ingevuld zal worden door de verbranding van primaire brandstoffen (in de tuinbouw vrijwel uitsluitend aardgas) in een ketel of een WKK-installatie. Tenbehoevevandebeschrijving vanderelatietussenwarmtebehoefte vandekas endeverbrandingvanprimairebrandstoffen zijninhetverwarmingssysteem simulatiemodel zes componenten onderscheiden. Dit zijn het verwarmingscircuit, de ketel, decondensor, deWKK-installatie, dewarmte-opslag tank enhetexpansievat.Vanuithetmodelconcept isdebeschrijving vanexpansievat nietvereistmaar dezeisaanhethoofdstuk toegevoegd omdat eenvandeenergiebesparende opties betrekking heeft op het expansievat. Het verwarmingscircuit is vanuit tuinbouwkundig oogpunt het belangrijkste onderdeel van het verwarmingssysteem. Om het dynamisch gedrag van dit onderdeel goed te kunnen beschrijven is een model ontwikkeld waarin de karakteristieke aspecten van zo'n circuit zijn opgenomen. De resultaten van dit model zijn vergeleken met gedetailleerde metingen aanhetverwarmingscircuit in een afdeling van een proefkas. De overeenkomst was erg goed.  228  Samenvatting Met betrekking tot de ketel is beargumenteerd dat voor dit onderdeel van het verwarmingssysteem een statisch model volstaat. De ketel wordt als onbeperkt regelbare vermogensbron beschouwd.Omdatvergroting van de ketelisolatiedikte 6envan de maatregelen is die in de MJA worden voorgesteld is de beschrijving vanwarmte-verliezen aan dewand vandeketel als functie van deisolatiediktein het model opgenomen. Van de condensor is bekend dat het energie besparend effect afhangt van de ingaandewatertemperatuur,dedoorstroomsnelheidvanderookgassenendebranderafstelling van de ketel. Deze invloedsfactoren zijn gekwantificeerd en in een statisch condensor-model ondergebracht. De WKK-installatie is,net als de ketel, beschouwd als warmtebron waarin geen rekening hoeft te worden met de dynamica van het systeem. Hetlaatstebelangrijke onderdeelvanhetverwarmingssysteem isdewarmte-opslag tank. Detoepassingvan zo'n tank krijgt mime aandacht in deuitwerking van de voorstellen in het kader van de MJA. Daarom wordt in dit werk een uitgebreid dynamisch model voor de beschrijving van het dynamisch gedrag van dit onderdeel van het verwarmingssysteem gepresenteerd. Dit model is vergeleken met metingen aan een proef-opstelling. Het model bleekhet gedragvan detank goed te beschrijven. Tenslotte wordt inhoofdstuk 4eenrekenschema opgesteld waarmee deverschillende onderdelen op elkaar worden aangesloten. Inhoofdstuk 5wordthetgebruiktekasklimaatmodelgepresenteerd.Hetkasklimaat is detweede hoofdcomponent van het simulatiemodel. In het model is expliciete aandacht besteed aan assimilatiebelichting en energieschermen. Het kasklimaatmodel is opgedeeld in een C02-model, een vocht-model en een thermisch model. Inhoofdstuk 6worden deresultaten vanhetcomplete simulatiemodel vergeleken met gedetailleerde en langetermijn metingen ineenproefkas met belichterozen. De gedetailleerde vergelijking is uitgevoerd aan de hand van 10 minuten gemiddelde meetwaarden over een periode van drie dagen injanuari 1995. De vergelijkingen betreffen de kasluchtcondities met betrekking tot temperatuur, vochtdeficit en C02-concentratie, pijptemperaturen en warmtevraag. Degesimuleerdewaarden endynamiek kwamenerggoedovereen met demetingen,hoewel er ook enkele opmerkelijke verschillen konden worden waargenomen. Ookzijn degesimuleerde kasklimaatregelaar-akties vergeleken met deaktiesvan deregelaar indeproefkas. Raamopening,schermregeling en assimilatiebelichting werden goed gesimuleerd. De regeling van de C02-dosering gaf verschillen te zien.  229  Samenvatting Demodelresultaten over een langeperiode zijn bestudeerd aan dehand vanjaarrondmetingen van de kasluchttemperatuur, het energieverbruik en de gewasverdamping. De kasluchttemperatuur werd goed beschreven, met uitzondering van zeer warme perioden. Gedurende die perioden berekende het model te hoge temperaturen. Hetgesimuleerde waterverbruik vanhetgewaskwamgoedovereen met het gemeten verbruik inhet najaar en inde winter. Inhet voorjaar enzomer berekende het model te hoge waterverbruiken. Het energieverbruik werd goed beschreven. Het gesimuleerde jaarverbruik was slechts 2% lager dan het gemeten verbruik. Nadat dekwaliteit van het simulatiemodel isgedemonstreerd aan dehand vande metingen in de proefkas ishet model toegepast ten behoeve van de beoordeling vanenergiebesparendemaatregelen.Daartoewerdendeparametersvanhetmodel gebaseerd op de bedrijfsuitrusting van een tomatenteelt in een moderne NederlandseVenlo-kasvaneenhectare.Hetverwarmingssysteem werdverondersteld te zijn uitgerust met een condensor en een warmte-opslagtank van 80 m3. De kasklimaatregelaar werd ingesteld volgens gangbare inzichten. Deteeltbestreek een periode van 1december tot 15november. Er werd gebruikt gemaakt van typisch Nederlands weer. De eerste categorie energiebesparende maatregelen diemet hetmodel zijn bestudeerd betreft eenvoudige maatregelen inhet ketelhuis.Hieronder vielen ketel- en pijpisolatie endeaansluitingvanhetexpansievat. Ten behoevevandeberekening van de effecten van pijpisolatie werden zes pijp-typen onderscheiden naar hun functie in hetverwarmingssysteem. De berekening van energie-verliezen aan het expansievatzijnuitgevoerd voordereferentiekas (meteenwarmte-opslagtank) en voor een kas zonder opslagtank. Het blijkt dat de energie-besparing die met deze eenvoudige maatregelen kan worden gerealiseerd kleinis.Echter, omdathetomrelatief goedkopemaatregelen gaat kunnen ze toch voordel opleveren. Detweedeclustervanenergiebesparende maatregelen diebestudeerd is,betreft de verminderingvanenergieverliezen aanhetkasdekmiddelsverminderdelekverliezen door ramen, de toepassing van een energieschermen, de verhoging van de isolatiewaarde van het kasbedekkingsmateriaal. Heteffect vanverminderde lekverliezen door deramen isbepaald door het energieverbruik van een kas waarvan 20%van de ramen altijd minimaal 1cm open bleven staan tevergelijken met datvan dereferentiekas. Het verschil inenergieverbruik bleek klein (1.6%). Het gebruik van een energiescherm leverde een energiebesparing op van23%. Echter, doordat het scherm-pakket inopgevouwen toestand 4%lichtonderscheppinggeeft, resulteert eenenergiescherm ook in eenverminderde gewasopbrengst. 230  Samenvatting Ombeideeffecten ineenkentalsamentevattenzijnde energiebesparings-effecten van maatregelen die invloed hebben op de gewasproduktie beoordeeld op grond van hun effect op het specifiek energieverbruik. Het specifiek energieverbruik is gedefinieerd alsjaarlijks primair energieverbruik per eenheid jaarphotosynthese. Hetspecifiek energieverbruik wordt uitgedrukt inMJkg"1.Uitgedrukt in specifiek energieverbruik leverde een energiescherm een besparing van20%. Metbetrekkingtot debestudering van deeffecten vanhoog-isolerende kasbedekkings-materialen is het model geschikt gemaakt voor de beschrijving van een dubbel glaskasdekenvoorverschillende typen coatingsopenkelen dubbel glas. Deenergie-besparingen diehierdoorwerdenbehaaldvarieerdenvan 18%(eentinoxide coating) tot 47% (een optie waarin een kasdek van dubbel-gecoat dubbel glaswerdverondersteld). Demeestevan dealternatieve kasbedekkingsmaterialen resulteren echter ook in een verminderde lichtdoorlatendheid. Wordt dit effect meegenomen, door het effect van deze materialen op het specifiek verbruik te berekenen, dan varieerden de besparingspercentages van 10% (een tin-oxide coating) tot 39%(dubbel-gecoat dubbel glas). Een neven-effect van de toepassing van kasbedekkingsmaterialen met een verhoogde isolatiegraad is de (absolute en relatieve) toename van de hoeveelheid energie diewordt gebruikt voor de vochtbeheersing in dekas. Dit effect is voor elk van de opties gekwantificeerd. De berekeningen lieten zien dat het absolute energiegebruik ten behoevevan devochtbeheersing indezwaarstge'isoleerdekas bijna twee maal zo groot was alsvoor de referentie-kas. De derde cluster van energiebesparende maatregelen betreft het gebruik van een condensor, eenwarmte-opslagtank en eenwarmtekracht-installatie (WKK-installatie).Heteffect vandecondensorwerd berekendvoortweewijzen van inpassing in het verwarmingssysteem. Het bleek dat het een voordeel oplevert, indien de condensor niet alleen op het secundair verwarmingscircuit, maar ook op het primaire verwarmingscircuit kan worden aangesloten. Heteffect vandetoepassingvaneenwarmte-oplagtank isbestudeerd vooreenkas zondereenkasmeteenWKK-installatie.InhetlaatstegevalwerddeWKK-installatie gebruikt voor de elektriciteitsvoorziening van de assimilatiebelichting. Voor kassen zonder WKK-installatie wordt de warmte-opslagtank gebruikt om warmtedievrijkomt bijdeC02-doseringmetketelrookgassen opteslaanvoorgebruik tijdens de nacht. Afhankelijk van de C02-doserings strategic uit het effect van de opslagtank zich vooral in energiebesparing of in produktieverhoging. Warmte-opslagverminderthetenergieverbruik alsdeC02-dosering onafhankelijk is van de actuele warmtevraag. In dat geval worden warmte-overschotten in de tank opgeslagen in plaats van door vergrootte ventilatie te worden vernietigd. Is deC02-dosering strategiczodanig datwarmtevemietigingwordtvoorkomen, dan zaleen warmte-opslagtank leidentot eenverhoogde C02-gift, endaarmeetoteen 231  Samenvatting verhoogde produktie. Ook hier kunnen beide effecten onder een noemerworden gebracht door de energiegebruikseffecten uit te drukken in termen van specifiek energieverbruik.Dezeberekeningenzijngemaaktvoorbeidedoseer-strategieen en voor drie doseersnelheden. Voor eenbedrijfssituatie waarin eenWKK-installatiede elektriciteitsvoorziening vandeassimilatiebelichtingverzorgt,bei'nvloedteenwarmte-opslagtankzowelhet energieverbruik alshetproduktieniveau,aangenomendatC0 2wordtgedoseerdzolangdeafValwarmte nietvernietigdhoeftteworden.Deberekeningentoondenaan dat het produktie-effect groter is dan het energiebesparings-effect. Wanneer een WKK-installatie elektriciteit produceert voor het openbaar net,dan levert dit een energiebesparing op omdat het totaal-rendement van de conversie van aardgas naar warmte en kracht (elektriciteit) van een dergelijke installatie hoger isdanwanneer aardgas incentraleswordt omgezet inelektriciteit enophet tuinbouwbedrijf in warmte. Het energiebesparings-effect wordt echter alleen zichtbaar als de vermindering van het gasverbruik van centrales (door elektriciteitsproduktie bijkassen)indebeschouwingwordt meegenomen.Het gasverbruik op het tuinbouwbedrijf stijgt bij de toepassing van WKK namelijk aanzienlijk. De energiebesparing die voortvloeit uit de toepassing van WKK hangt voor het grootste geheel af van de capaciteit van de WKK-installatie (het elektrisch vermogen per m2 kasoppervlak). De berekeningen laten zien dat door de toepassingvanWKKbesparingspercentages tot32%kunnenworden behaald.Indien derookgassen van WKK-installatiesvoldoende zuiver zouden zijn om toegepast te kunnen worden als C02-bron in plaats van ketelrookgassen kunnen de besparingspercentages nog verder toenemen. In hoofdstuk 7worden de conclusies getrokken uit de analyses die in het kader van dit proefschrift hebben plaatsgevonden. Enkele punten daaruit worden nader bediscussieerd.  232  Curriculum vitae CURRICULUM VITAE Hendrik Feije de Zwart werd op 29januari 1965 te Bennebroek geboren. Van 1967 tot 1971 en van 1972 tot 1976 woonde hij in Indonesie. Het grootste deel van zijn lagere school-tijd viel in detweede periode van vierjaar. In diejaren is hij, samen met zijn eenjaarjongere broer, door zijn moeder onderwezen. Terug in Nederland vond hij een goede aansluiting met de zesde klas van de lagere school. Na de lagere school doorliep hij het Atheneum van de 'scholengemeenschap LeidenZuid-West',waarvandenaamin 1978veranderde in'DeVlietschans'.Het VWO-diploma behaalde hij in 1983. Indatzelfdejaar begonhij zijn wetenschappelijke opleiding aandeLandbouwhogeschool te Wageningen, waarvan de naam in zijn studieperiode overging naar Landbouwuniversiteit Wageningen. Injanuari 1989 behaalde hij aldaar het doctoraalexamen in de studierichting Landbouwtechniek (vrije orientatie). Zijn afstudeervakken betroffen modelvorming ensimulatie (6maanden) en regeltechniek (eveneens 6maanden). Na een korteperiode alsprakticumleider bij devakgroep Natuur- en Weerkunde van de Landbouwuniversiteit Wageningen te hebben gewerkt, begon hij in december 1989bij IMAG-DLO aan het onderzoek dat uiteindelijk tot dit proefschrift heeft geleid. Sinds begin 1996 werkt hij daar in een dienstverband voor onbepaalde tijd binnen de afdeling Energietechniek.  233  Dankwoord DANKWOORD Op de middelbare school leerde ik dat er drie vereisten zijn voor de totstandkomingvan eenprodukt, namelijk kapitaal, arbeid enondememingszin. Wat betreft heteersteisdetotstandkomingvanditproefschrift tedankenaandefinanciele bijdragevanNOVEM(Nederlandse OndememingVoorEnergie enMilieubv)ende middelen die door IMAG-DLO beschikbaar zijn gesteld. Detweeanderedoorslaggevende factoren kunnenvrij worden vertaald mettranspiratie eninspiratie.Inspiratie zou ik daarbij voorop willen stellen omdat dateen voorwaarde is omje niet door transpiratie te latenweerhouden. Voor wat betreft die inspiratie ben ikveel dank verschuldigd aan de mensen die deafgelopenjaren bijhet onderzoek rond ditproefschrift betrokken zijn geweest. Het moet voor mijn naaste collega, Jo Huijs, en mijn begeleiders Gerard Bot en Bert Speelmannietgemakkelijk geweestzijn omalsgesprekspartner optetreden enmij feed-back tegeven,gezienmijn zwalkendeideeenoveraanpak,richtingen inhoudvanditonderzoek. Velemalengingdezaakopdeschopenwerden ideeen dieeerst zinvol lekenomuitgewerkt teworden bijdevolgendebijeenkomst weer als irrelevant of oninteressant door mij van dehand gewezen. De flexibiliteit die zij daarin opbrachten is bewonderenswaardig en ik ben blij dat zij telkens toch weer hun vertrouwen in mijn werk hebben getoond. De drie genoemde meest betrokkenen hebben alien op hun eigen wijze hun bijdrage doen gelden. Heel praktisch heeft Jo me gezond gehouden met een dagelijks stukje fruit. Ook depaar stressige dagen,voorafgaand aande dead-line waarop hetproefschrift naar dedrukker moest, heeft hij enorm veel werk verzet in het opmaken en inplakken van de grafieken en figuren. Zonder zijn inzetwas hetnietoptijd klaargeweest.Inhoudelijk wasJo,door zijn globalistische kijkop mijnonderzoek,eenprettigeenkritischegesprekspartner.Heelwatinconsistenties, modellerings-enrekenfouten kwamenaanhetlichtdoorzijnvragen enopmerkingen. Daarnaast heeft hij in de eerstejaren van het onderzoek, als leider van het project waar mijn werk een onderdeel van vormde, alle management-activiteiten eeneffectieve wijze gestaltegegeven.Wewareneensterk teamenikhoopdatdat nog een aantaljaren kan worden voortgezet. Gerard Bot wil ik met name bedanken voor zijn grondige bestudering van alle concept-hoofdstukken die in de loop derjaren door mij werden ge-of herschreven. Het moet je veel tijd gekost hebben. Daarnaast is mij door hem veel vakinhoudelijke kennis bijgebracht. Bert Speelman wilikbedanken voordetijd enaandachtdiehij ondankszijn voile agendaaanmijheeftbesteed.Debegeleidingsgesprekken metjouenGerardwaren altijd opbouwend en stimulerend. Na zo'n begeleidingsbijeenkomst vervolgde ik telkens met hemieuwd elan mijn werk. Graag wil ik op deze plek ook mijn collega's van de gang bedanken voor de 235  Dankwoord plezierigewerksfeer diedoorhen gestaltekrijgt. RinusTelle,vanwegezijn schier onuitputtelijke bron van citaten en anekdotes, Jo Huijs, op deze plaats nogmaals genoemd vanwege zijn positieve invloed op de werksfeer, Nico van de Braak, vanwegezijn welgemeendebelangstellingennuchtere relativeringen, Peter Knies vanwegezijn praktische enpragmatische instelling(hij bedachthethandelsmerk KASPRO - voor het simulatieprogramma dat in dit proefschrift beschreven staat), Jo Breuer vanwege zijn uitgebreid archief en Frank Kempkes vanwege zijn vocabulaire kunstzinnigheden. Steef van Aggelen en Ferry Corver wil ik bedanken voor hun teeltkundige bijdrage aandemetingeninkassen.ReinBijkerk enHansJansenben ikdankbaar omhun alerte bewaking van decontinui'teitin deverzameling vanmeetgegevens enHennyvanDorlandenAppieBaadillavoordeondersteuning inhetaanbrengen van aanpassingen in de kas en het meet-systeem. Tenslotte noem ikJan Selten enHarry Oldenhof vanwege detips entrues diezij mij op software-gebied aanreikten. Nietvanwegehunbijdrage aande inhoudelijke kant vanhetwerk, maarvanwege de morele steun en interesse die ik van hen ondervond wil ik graag mijn dank betuigen aan vrienden en familie. Ik was altijd een beetje vaag over wat ik nou precies aan het doen was, maar dat heeft jullie er niet van weerhouden toch regelmatig te informeren naar de stand van zaken, maar vooral naar mijn subjectieve belevingdaarin.Hierinwil ikspeciaalMariette noemenomdatzij mij telkens weer over momenten van twijfel heeft heengeholpen. Tenslotte wilikMariettenogmaalsnoemen omdat zij mijn leveninhetalgemeen gelukkig maakt.  236